Aula 3: Álgebra matricial 3 e Análise dos Componentes ... · Web viewAula 3: Álgebra matricial 3...
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Aula 3: Álgebra matricial 3 e Análise dos Componentes Principais (PCA) José Ricardo Inacio Ribeiro Isso é um R Markdown Notebook depositado no Bioforum. Quando executar o código, os resultados aparecerão abaixo dele! Vetores V1 <- as.vector ( seq ( 1 , 10 )) V1 ## [1] 1 2 3 4 5 6 7 8 9 10 V2 <- as.vector ( seq ( 11 , 20 )) V2 ## [1] 11 12 13 14 15 16 17 18 19 20 _______exercício 7________: Existe outra forma de fazer isso? # Podemos adicionar uma constante a cada elemento: V4 <- V1 + 20 V4 ## [1] 21 22 23 24 25 26 27 28 29 30 # Ou podemos adicionar cada elemento do primeiro vetor ao elemento correspondente do segundo vetor V3 <- V1 + V2 V3 ## [1] 12 14 16 18 20 22 24 26 28 30 # Multiplicação de vetores por um escalar: V2 <- 4 * V1 V2 ## [1] 4 8 12 16 20 24 28 32 36 40
Transcript of Aula 3: Álgebra matricial 3 e Análise dos Componentes ... · Web viewAula 3: Álgebra matricial 3...
Aula 3: Álgebra matricial 3 e Análise dos Componentes Principais (PCA)
José Ricardo Inacio Ribeiro
Isso é um R Markdown Notebook depositado no Bioforum. Quando executar o código, os resultados aparecerão abaixo dele!
VetoresV1 <- as.vector(seq(1, 10))V1
## [1] 1 2 3 4 5 6 7 8 9 10
V2 <- as.vector(seq(11, 20))V2
## [1] 11 12 13 14 15 16 17 18 19 20
_______exercício 7________:
Existe outra forma de fazer isso?
# Podemos adicionar uma constante a cada elemento:V4 <- V1 + 20V4
## [1] 21 22 23 24 25 26 27 28 29 30
# Ou podemos adicionar cada elemento do primeiro vetor ao elemento correspondente do segundo vetorV3 <- V1 + V2V3
## [1] 12 14 16 18 20 22 24 26 28 30
# Multiplicação de vetores por um escalar:V2 <- 4 * V1V2
## [1] 4 8 12 16 20 24 28 32 36 40
# Multiplicação de vetores onde cada elemento de um vetor é multiplicado pelo seu correspondente no outro vetor:V1 * V2
## [1] 4 16 36 64 100 144 196 256 324 400
# Produto externo (lembre-se que o operador de multiplicação de matrizes é %*%):V1 <- seq(1, 10)V2 <- seq(1, 4)V1
## [1] 1 2 3 4 5 6 7 8 9 10
V2
## [1] 1 2 3 4
prod.ext <- V1 %*% t(V2) #temos que fazer a transpostaprod.ext
## [,1] [,2] [,3] [,4]## [1,] 1 2 3 4## [2,] 2 4 6 8## [3,] 3 6 9 12## [4,] 4 8 12 16## [5,] 5 10 15 20## [6,] 6 12 18 24## [7,] 7 14 21 28## [8,] 8 16 24 32## [9,] 9 18 27 36## [10,] 10 20 30 40
$\color{red}{\text{Temos que fazer a transposta porque $X_{n \times 1} \times Y_{1 \times m} = (XY)_{n \times m}$, segundo a figura abaixo:}}$
O produto interno é uma operação muito útil, porque ele não só multiplica cada elemento correspondente de dois vetores mas também soma o produto resultante:
pr odu t o−i n t er no=∑i=1
N
V 1i×V 2i
V1 <- seq(1, 10)V2 <- seq(11, 20)V1
## [1] 1 2 3 4 5 6 7 8 9 10
V2
## [1] 11 12 13 14 15 16 17 18 19 20
in.prod <- t(V1) %*% V2in.prod #uma matriz de uma linha e uma coluna!
## [,1]## [1,] 935
Podemos normalizar vetores a partir do cálculo do produto-interno de um vetor. Norma de um vetor é seu comprimento. Vamos calcular a raiz quadrada do seu produto-interno:
¿∨a∨¿=¿
V1 <- seq(1, 10)V1
## [1] 1 2 3 4 5 6 7 8 9 10
in.prod <- t(V1) %*% V1in.prod #uma matriz de uma linha e uma coluna!
## [,1]## [1,] 385
sqrt(in.prod)
## [,1]## [1,] 19.62142
#vetor normalizado:V1.n <- V1 / as.vector(sqrt(in.prod))V1.n
## [1] 0.05096472 0.10192944 0.15289416 0.20385888 0.25482360 0.30578831## [7] 0.35675303 0.40771775 0.45868247 0.50964719
_______exercício 8________:
Qual o comprimento do vetor V1.n?
Cálculo da variância usando vetores:V <- V1V
## [1] 1 2 3 4 5 6 7 8 9 10
# Preciso calcular a média de todos os números em um vetor. Para tanto, (1) precisamos somar# os números (com o produto-interno do vetor com um vetor de algarismos 1):uns <- rep(1, length(V))uns
## [1] 1 1 1 1 1 1 1 1 1 1
soma.V <- t(uns) %*% Vsoma.V
## [,1]## [1,] 55
# (2) Agora, dividimos pelo número de elementos de V:media.V <- soma.V * (1/length(V))media.V
## [,1]## [1,] 5.5
# Colocando tudo junto:media.V <- t(uns) %*% V * (1/length(V))media.V
## [,1]## [1,] 5.5
# ou:mean(V)
## [1] 5.5
# (3) A variância é o desvio-quadrado médio da média. Assim, (A) precisaremos achar# os desvios da média subtraindo a média de cada valor do vetor:V - as.vector(media.V)
## [1] -4.5 -3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5 4.5
# (B) Então, achamos a variância como o quadrado médio a partir do produto-interno:Var.V <- t(V - as.vector(media.V)) %*% (V - as.vector(media.V)) * (1/(length(V) - 1))Var.V
## [,1]## [1,] 9.166667
# ou:var(V)
## [1] 9.166667
Matrizes (combinção de vetores):Xc <- cbind(V1, V2, V3) #por colunasXc
## V1 V2 V3## [1,] 1 11 12## [2,] 2 12 14## [3,] 3 13 16## [4,] 4 14 18## [5,] 5 15 20## [6,] 6 16 22## [7,] 7 17 24## [8,] 8 18 26## [9,] 9 19 28## [10,] 10 20 30
dim(Xc)
## [1] 10 3
Xr <- rbind(V1, V2, V3) #por linhasXr
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]## V1 1 2 3 4 5 6 7 8 9 10## V2 11 12 13 14 15 16 17 18 19 20## V3 12 14 16 18 20 22 24 26 28 30
dim(Xr)
## [1] 3 10
Como em vetores, podemos somar, subtrair, multiplicar e dividir a matriz por um escalar: Dada a matriz
A=[ 3 810 4 ]
Então, a operação 5A, onde o escalar é representado pelo número 5, é dada por…
5 A=5×[ 3 810 4]=[15 40
50 20 ]Da mesma forma, dado o escalar $ $, a operação $ $A é dada por…
λ A=λ×[ 3 λ 8 λ10 λ 4 λ]
É importante lembrar que, se a matriz tem um fator comum, esse fator pode ser extraído da matriz e tratado como um escalar…
[15 4050 20 ]=5 [ 3 8
10 4]=¿
Assim, se
A=¿ai j∨¿
e
λ
é um escalar, temos…
λ A=A λ=¿ λai j∨¿
Operações:Xc + 4 #adição
## V1 V2 V3## [1,] 5 15 16## [2,] 6 16 18## [3,] 7 17 20## [4,] 8 18 22## [5,] 9 19 24## [6,] 10 20 26## [7,] 11 21 28## [8,] 12 22 30## [9,] 13 23 32## [10,] 14 24 34
round((Xc + 4) / 3, 2) #arredondando os valores
## V1 V2 V3## [1,] 1.67 5.00 5.33## [2,] 2.00 5.33 6.00## [3,] 2.33 5.67 6.67## [4,] 2.67 6.00 7.33## [5,] 3.00 6.33 8.00## [6,] 3.33 6.67 8.67## [7,] 3.67 7.00 9.33## [8,] 4.00 7.33 10.00## [9,] 4.33 7.67 10.67## [10,] 4.67 8.00 11.33
# Nós podemos multiplicar cada linha (ou coluna) por um vetor!V
## [1] 1 2 3 4 5 6 7 8 9 10
Xc * V
## V1 V2 V3## [1,] 1 11 12## [2,] 4 24 28## [3,] 9 39 48## [4,] 16 56 72## [5,] 25 75 100## [6,] 36 96 132## [7,] 49 119 168## [8,] 64 144 208## [9,] 81 171 252## [10,] 100 200 300
Multiplicação de matrizes (A×B):
x y i j=∑k=1
n
x i k× y j k
n <- dim(Xc)[1] # número de linhasuns <- rep(1, n)uns
## [1] 1 1 1 1 1 1 1 1 1 1
length(uns)
## [1] 10
X.med <- t(uns) %*% Xc / nX.med
## V1 V2 V3## [1,] 5.5 15.5 21
#oucolMeans(Xc)
## V1 V2 V3 ## 5.5 15.5 21.0
Variâncias e covariâncias são medidas de dispersão ao redor da média! Podemos calculá-las subtraindo as médias de todas as observações. Com isso, teremos uma matriz centrada. Usaremos o artifício da matriz de algarismos um…
X.diff <- Xc - uns %*% X.medX.diff #uma matriz centrada
## V1 V2 V3## [1,] -4.5 -4.5 -9
## [2,] -3.5 -3.5 -7## [3,] -2.5 -2.5 -5## [4,] -1.5 -1.5 -3## [5,] -0.5 -0.5 -1## [6,] 0.5 0.5 1## [7,] 1.5 1.5 3## [8,] 2.5 2.5 5## [9,] 3.5 3.5 7## [10,] 4.5 4.5 9
Agora, calculamos o produto-interno da matriz centrada pelas médias com ela mesma! O resultado, dividiremos por n−1.
_______exercício 9________:
Como fazemos isso?
A diagonal de uma matriz de variância-covariância contém a variância!X.cov <- t(X.diff) %*% X.diffX.cov <- X.cov / (n - 1)round(X.cov, 2)
## V1 V2 V3## V1 9.17 9.17 18.33## V2 9.17 9.17 18.33## V3 18.33 18.33 36.67
dim(X.cov) #3x3
## [1] 3 3
#ou simplesmente:cov(Xc)
## V1 V2 V3## V1 9.166667 9.166667 18.33333## V2 9.166667 9.166667 18.33333## V3 18.333333 18.333333 36.66667
diag(X.cov) #a diagonal é a variância
## V1 V2 V3 ## 9.166667 9.166667 36.666667
$\color{red}{\text{Portanto, podemos converter a matriz de variância-covariância em uma matriz de correlação!}}$ Lembre-se: r x y=c ov x y /√V xV y
# Multiplicaremos antes e depois a matriz pela diagonal contendo o recíproco # dos desvios-padrão (a raiz quadrada das variâncias):sdi <- diag(1 / sqrt(diag(X.cov))) #criamos uma matrizsdi #desvios-padrão
## [,1] [,2] [,3]## [1,] 0.3302891 0.0000000 0.0000000## [2,] 0.0000000 0.3302891 0.0000000## [3,] 0.0000000 0.0000000 0.1651446
dim(sdi) # 3x3
## [1] 3 3
#3x3 X 3x3 X 3x3X.cor <- sdi %*% X.cov %*% sdiX.cor
## [,1] [,2] [,3]## [1,] 1 1 1## [2,] 1 1 1## [3,] 1 1 1
#ou simplesmente:cor(Xc)
## V1 V2 V3## V1 1 1 1## V2 1 1 1## V3 1 1 1
Determinante de uma matriz quadrada:
±(ad−bc)A <- matrix(c(1, 2, 3, 4), byrow = T, nc = 2)A
## [,1] [,2]## [1,] 1 2## [2,] 3 4
# O determinante, segundo a fórmula, será...(A[1,1] * A[2,2]) - (A[1,2] * A[2,1]) # -2
## [1] -2
#ou:det(A) # -2
## [1] -2
Vejamos o que acontece com o determinante de uma matriz em uma matriz que tenha suas colunas linearmente dependentes# uma matriz com colunas linearmente dependentes:A <- matrix(c(1, 2, 2, 4), byrow = T, nc = 2)A
## [,1] [,2]## [1,] 1 2## [2,] 2 4
dim(A)
## [1] 2 2
É fácil observar que a segunda coluna é um múltiplo da primeira. A relação entre a primeira e segunda coluna pode ser escrita como…
[24 ]=2 [12]=¿
$\color{red}{\text{O conceito de posto de uma matriz está ligado intimamente à questão da dependência linear, porque o posto é o número máximo de}}$$\color{red}{\text{colunas ou linhas linearmente INDEPENDENTES de uma matrix}}$
_______exercício 9________:
Qual é o posto da matriz A?
O determinante de A será zero!
det(A)
## [1] 0
$\color{red}{\text{Importante: quando uma matriz tem determinante igual a zero, dizemos que a matriz é SINGULAR!}}$
Praticando PCA no R…# fazendo no shapes:require(geomorph)
## Loading required package: geomorph
## Loading required package: rgl
## Loading required package: ape
library(shapes)tudo1 <- readland.tps(file = '~/Dropbox/aulas/Morfogeo/morfo_aulas/alunos_landmark/folhasok.TPS', specID = 'ID')
## ## No curves detected; all points appear to be fixed landmarks.## ## Warning: not all specimens have scale adjustment (perhaps because they are already scaled);## no rescaling will be performed in these cases
#configurações sobrepostas e projeção no espaço tangentesup <- procGPA(tudo1)tudo1 <- sup$tan # no espaço tangente# guardando o tamanho do centroidesize<-sup$size
#fazendo no geomorph:library(geomorph)tudo1 <- readland.tps(file = '~/Dropbox/aulas/Morfogeo/morfo_aulas/alunos_landmark/folhasok.TPS', specID = 'ID')
## ## No curves detected; all points appear to be fixed landmarks.## ## Warning: not all specimens have scale adjustment (perhaps because they are already scaled);## no rescaling will be performed in these cases
tudo1 #um array
## , , ori1 ## ## [,1] [,2]## [1,] 497 1068
## [2,] 499 1146## [3,] 1121 1927## [4,] 1813 1760## [5,] 1980 1670## [6,] 2238 1545## [7,] 2423 1430## [8,] 2577 1319## [9,] 2980 1136## [10,] 2631 941## [11,] 2442 785## [12,] 2245 657## [13,] 2031 485## [14,] 1741 353## [15,] 1103 248## ## , , ori2 ## ## [,1] [,2]## [1,] 905 940## [2,] 912 1016## [3,] 1448 1638## [4,] 1815 1563## [5,] 2084 1442## [6,] 2273 1329## [7,] 2444 1215## [8,] 2592 1080## [9,] 2807 897## [10,] 2498 705## [11,] 2383 610## [12,] 2287 553## [13,] 2009 431## [14,] 1807 358## [15,] 1368 294## ## , , ori3 ## ## [,1] [,2]## [1,] 833 942## [2,] 834 991## [3,] 1330 1626## [4,] 2002 1460## [5,] 2157 1367## [6,] 2271 1283## [7,] 2416 1206## [8,] 2513 1130## [9,] 2790 1006## [10,] 2537 885## [11,] 2442 832## [12,] 2341 774## [13,] 2229 711
## [14,] 2138 653## [15,] 1273 350## ## , , ori4 ## ## [,1] [,2]## [1,] 636 963## [2,] 634 1062## [3,] 1237 1759## [4,] 2035 1564## [5,] 2161 1481## [6,] 2313 1380## [7,] 2556 1219## [8,] 2699 1108## [9,] 2974 936## [10,] 2689 844## [11,] 2485 679## [12,] 2281 572## [13,] 2022 426## [14,] 1870 362## [15,] 1244 285## ## , , ori5 ## ## [,1] [,2]## [1,] 631 892## [2,] 631 957## [3,] 1229 1591## [4,] 1635 1518## [5,] 1791 1462## [6,] 2076 1321## [7,] 2304 1183## [8,] 2471 1035## [9,] 2775 869## [10,] 2387 697## [11,] 2212 602## [12,] 1870 441## [13,] 1653 386## [14,] 1535 358## [15,] 1126 337## ## , , ori6 ## ## [,1] [,2]## [1,] 543 1067## [2,] 555 1131## [3,] 1342 1768## [4,] 1753 1615## [5,] 1914 1518## [6,] 2107 1375
## [7,] 2283 1254## [8,] 2445 1123## [9,] 2737 962## [10,] 2510 858## [11,] 2389 747## [12,] 2215 631## [13,] 2052 505## [14,] 1712 381## [15,] 1042 286## ## , , ori7 ## ## [,1] [,2]## [1,] 834 945## [2,] 840 1031## [3,] 1489 1714## [4,] 2188 1376## [5,] 2280 1321## [6,] 2381 1247## [7,] 2447 1176## [8,] 2562 1066## [9,] 2808 809## [10,] 2474 650## [11,] 2355 554## [12,] 2172 462## [13,] 2091 430## [14,] 1772 352## [15,] 1322 301## ## , , ori8 ## ## [,1] [,2]## [1,] 553 943## [2,] 555 1026## [3,] 1089 1710## [4,] 1627 1634## [5,] 1774 1581## [6,] 2064 1462## [7,] 2263 1297## [8,] 2410 1154## [9,] 2748 898## [10,] 2312 753## [11,] 2146 656## [12,] 1917 542## [13,] 1770 450## [14,] 1638 415## [15,] 1038 373## ## , , ori9##
## [,1] [,2]## [1,] 494 1040## [2,] 490 1068## [3,] 1584 1359## [4,] 2157 1266## [5,] 2366 1208## [6,] 2474 1150## [7,] 2530 1104## [8,] 2645 1042## [9,] 2692 983## [10,] 2669 911## [11,] 2563 826## [12,] 2342 692## [13,] 2080 580## [14,] 1783 570## [15,] 1588 570## ## , , ori10## ## [,1] [,2]## [1,] 661 820## [2,] 613 843## [3,] 1491 1181## [4,] 1905 1126## [5,] 2028 1075## [6,] 2142 1010## [7,] 2271 905## [8,] 2387 825## [9,] 2430 768## [10,] 2382 730## [11,] 2256 672## [12,] 2176 612## [13,] 1970 525## [14,] 1839 506## [15,] 1478 511## ## , , ori11## ## [,1] [,2]## [1,] 379 1058## [2,] 394 1094## [3,] 1348 1431## [4,] 1979 1314## [5,] 2146 1232## [6,] 2228 1193## [7,] 2371 1072## [8,] 2427 1026## [9,] 2459 963## [10,] 2386 913## [11,] 2327 889
## [12,] 2242 841## [13,] 2170 785## [14,] 2039 732## [15,] 1315 689## ## , , ori12## ## [,1] [,2]## [1,] 548 1018## [2,] 548 1046## [3,] 1551 1413## [4,] 2180 1272## [5,] 2290 1204## [6,] 2366 1136## [7,] 2416 1085## [8,] 2467 1038## [9,] 2486 982## [10,] 2432 960## [11,] 2371 929## [12,] 2233 857## [13,] 2038 767## [14,] 1861 699## [15,] 1515 676## ## , , ori13## ## [,1] [,2]## [1,] 688 741## [2,] 711 770## [3,] 1553 1052## [4,] 1974 964## [5,] 2072 923## [6,] 2155 867## [7,] 2199 835## [8,] 2248 801## [9,] 2284 753## [10,] 2251 710## [11,] 2189 665## [12,] 2116 621## [13,] 1999 560## [14,] 1921 529## [15,] 1568 450## ## , , ori14## ## [,1] [,2]## [1,] 648 736## [2,] 623 766## [3,] 1419 1036## [4,] 1630 1020
## [5,] 1846 939## [6,] 1973 848## [7,] 2032 791## [8,] 2072 723## [9,] 2077 676## [10,] 2057 642## [11,] 2003 602## [12,] 1913 554## [13,] 1829 520## [14,] 1731 496## [15,] 1394 495## ## , , ori15## ## [,1] [,2]## [1,] 721 867## [2,] 721 893## [3,] 1549 1123## [4,] 1726 1107## [5,] 1826 1069## [6,] 1902 1036## [7,] 2018 955## [8,] 2055 895## [9,] 2062 860## [10,] 2050 810## [11,] 2011 768## [12,] 1933 710## [13,] 1832 655## [14,] 1648 625## [15,] 1545 622## ## , , ori16## ## [,1] [,2]## [1,] 943 743## [2,] 940 770## [3,] 1722 1007## [4,] 2027 925## [5,] 2104 878## [6,] 2169 830## [7,] 2230 775## [8,] 2252 735## [9,] 2275 700## [10,] 2271 660## [11,] 2213 606## [12,] 2144 573## [13,] 2088 542## [14,] 2020 517## [15,] 1722 488
?gpagen#superimpose configurationssup <- gpagen(A = tudo1, ProcD = T, Proj = T)
## |
| | 0% |
|============= | 20% |
|========================== | 40% |
|=================================================================| 100%
names(sup)
## [1] "coords" "Csize" "iter" "points.VCV" ## [5] "points.var" "consensus" "p" "k" ## [9] "nsliders" "nsurf" "data" "Q" ## [13] "slide.method" "call"
sup$coords #coordenadas sobrepostas
## , , ori1 ## ## [,1] [,2]## [1,] -0.41141968 0.003584539## [2,] -0.41016829 0.026467190## [3,] -0.21769177 0.250135576## [4,] -0.01564311 0.194983654## [5,] 0.03292593 0.167000003## [6,] 0.10739529 0.127992550## [7,] 0.16075954 0.092448512## [8,] 0.20498298 0.058390595## [9,] 0.32084435 0.001126667## [10,] 0.21712019 -0.052791254## [11,] 0.16036732 -0.096743512## [12,] 0.10127709 -0.132588336## [13,] 0.03676838 -0.180990032## [14,] -0.04945354 -0.216951328## [15,] -0.23806468 -0.242064825## ## , , ori2
## ## [,1] [,2]## [1,] -0.40143371 -0.006744274## [2,] -0.39944299 0.021374951## [3,] -0.20093338 0.255603082## [4,] -0.06214992 0.229817899## [5,] 0.03777037 0.187077651## [6,] 0.10854744 0.146540412## [7,] 0.17265335 0.105409955## [8,] 0.22824572 0.056596184## [9,] 0.30895168 -0.009433858## [10,] 0.19659395 -0.082100492## [11,] 0.15445189 -0.118131103## [12,] 0.11853256 -0.140342335## [13,] 0.01695268 -0.187333026## [14,] -0.05759739 -0.215750591## [15,] -0.22114224 -0.242584456## ## , , ori3 ## ## [,1] [,2]## [1,] -0.447696463 -0.001780098## [2,] -0.446277897 0.016802720## [3,] -0.242630227 0.246282687## [4,] 0.007855693 0.169094198## [5,] 0.064665979 0.130582339## [6,] 0.106280830 0.096244886## [7,] 0.159560457 0.063799026## [8,] 0.194742426 0.032806576## [9,] 0.296474042 -0.020176662## [10,] 0.198346161 -0.060483320## [11,] 0.161089001 -0.078681424## [12,] 0.121272498 -0.098658631## [13,] 0.077146179 -0.120266880## [14,] 0.040894938 -0.140301347## [15,] -0.291723617 -0.235264069## ## , , ori4 ## ## [,1] [,2]## [1,] -0.42461617 -0.010518138## [2,] -0.42571742 0.020341522## [3,] -0.23865949 0.241182391## [4,] 0.01152129 0.184144309## [5,] 0.05163125 0.158737537## [6,] 0.09982253 0.127817385## [7,] 0.17638252 0.078717145## [8,] 0.22162288 0.044647729## [9,] 0.30822091 -0.007793855## [10,] 0.21971699 -0.038060211
## [11,] 0.15688391 -0.090447431## [12,] 0.09359703 -0.124923778## [13,] 0.01340323 -0.171725978## [14,] -0.03415039 -0.192514912## [15,] -0.22965908 -0.219603717## ## , , ori5 ## ## [,1] [,2]## [1,] -0.400859326 -0.018340000## [2,] -0.401587293 0.004556281## [3,] -0.193439703 0.234257306## [4,] -0.047330713 0.212279019## [5,] 0.008639234 0.193899822## [6,] 0.109555656 0.147611654## [7,] 0.190737098 0.101613849## [8,] 0.250754692 0.051636990## [9,] 0.358484905 -0.003377464## [10,] 0.225426908 -0.067611400## [11,] 0.165184004 -0.102996029## [12,] 0.047987566 -0.162848353## [13,] -0.027741688 -0.185071958## [14,] -0.070063147 -0.196631514## [15,] -0.215748192 -0.208978204## ## , , ori6 ## ## [,1] [,2]## [1,] -0.43001605 0.007508726## [2,] -0.42659477 0.028719032## [3,] -0.17032161 0.244590694## [4,] -0.03247324 0.197172376## [5,] 0.02153886 0.166371843## [6,] 0.08622355 0.120758358## [7,] 0.14513014 0.082110501## [8,] 0.19936750 0.040157379## [9,] 0.29638866 -0.010774668## [10,] 0.22233134 -0.046823086## [11,] 0.18313511 -0.084274950## [12,] 0.12650831 -0.123779754## [13,] 0.07343022 -0.166454845## [14,] -0.03730582 -0.209579465## [15,] -0.25734220 -0.245702143## ## , , ori7 ## ## [,1] [,2]## [1,] -0.42550079 -0.025281875## [2,] -0.42653854 0.005827410## [3,] -0.21518442 0.275583380
## [4,] 0.04891699 0.180467923## [5,] 0.08474374 0.163799525## [6,] 0.12437974 0.140611975## [7,] 0.15137943 0.117130550## [8,] 0.19695188 0.081665913## [9,] 0.29473308 -0.001349024## [10,] 0.18084857 -0.070685284## [11,] 0.14134353 -0.109685531## [12,] 0.07870396 -0.149661380## [13,] 0.04992561 -0.164625277## [14,] -0.06170597 -0.204386808## [15,] -0.22299682 -0.239411499## ## , , ori8 ## ## [,1] [,2]## [1,] -0.40217058 -0.018230880## [2,] -0.40164584 0.009784791## [3,] -0.21719529 0.242151571## [4,] -0.03368417 0.216584190## [5,] 0.01669642 0.198498082## [6,] 0.11438269 0.158600099## [7,] 0.18185223 0.103250204## [8,] 0.23175723 0.055194860## [9,] 0.34554301 -0.030296354## [10,] 0.19969767 -0.079873197## [11,] 0.14375026 -0.113032110## [12,] 0.06656938 -0.151974917## [13,] 0.01632866 -0.183527968## [14,] -0.02919172 -0.195888015## [15,] -0.23268995 -0.211240356## ## , , ori9## ## [,1] [,2]## [1,] -0.54219385 0.0001219051## [2,] -0.54411166 0.0100810695## [3,] -0.16517670 0.1342128620## [4,] 0.03831884 0.1118293164## [5,] 0.11280618 0.0951210641## [6,] 0.15223594 0.0764655430## [7,] 0.17333355 0.0609461246## [8,] 0.21496586 0.0410156570## [9,] 0.23330242 0.0207029637## [10,] 0.22559659 -0.0052883668## [11,] 0.18974033 -0.0371956147## [12,] 0.11469450 -0.0882356142## [13,] 0.02493600 -0.1324049077## [14,] -0.07892433 -0.1416903193## [15,] -0.14952367 -0.1456816827
## ## , , ori10## ## [,1] [,2]## [1,] -0.52439805 -0.003567778## [2,] -0.54526133 0.006141455## [3,] -0.16697203 0.159855361## [4,] 0.01337269 0.138921849## [5,] 0.06723178 0.117650950## [6,] 0.11728582 0.090236238## [7,] 0.17405603 0.045665767## [8,] 0.22494438 0.011794143## [9,] 0.24435497 -0.012792621## [10,] 0.22345655 -0.029818900## [11,] 0.16926917 -0.055992343## [12,] 0.13480169 -0.082706524## [13,] 0.04619262 -0.121993659## [14,] -0.01065480 -0.131331612## [15,] -0.16767949 -0.132062326## ## , , ori11## ## [,1] [,2]## [1,] -0.56076011 0.001366836## [2,] -0.55564178 0.015124697## [3,] -0.20288043 0.151688628## [4,] 0.03332742 0.113880041## [5,] 0.09652735 0.084850370## [6,] 0.12818050 0.070604583## [7,] 0.18274750 0.026877883## [8,] 0.20455198 0.009807475## [9,] 0.21819360 -0.013941172## [10,] 0.19050466 -0.033766301## [11,] 0.16820167 -0.043806427## [12,] 0.13627675 -0.062921982## [13,] 0.10902870 -0.084836911## [14,] 0.06005235 -0.105941480## [15,] -0.20831017 -0.128986239## ## , , ori12## ## [,1] [,2]## [1,] -0.56305122 -0.0217057856## [2,] -0.56360392 -0.0102612875## [3,] -0.16987770 0.1570619056## [4,] 0.08398738 0.1126682554## [5,] 0.12982204 0.0874466215## [6,] 0.16223313 0.0614531403## [7,] 0.18399459 0.0415411011## [8,] 0.20579271 0.0232854551
## [9,] 0.21566079 0.0006547272## [10,] 0.19341524 -0.0098659570## [11,] 0.16910922 -0.0238908120## [12,] 0.11503848 -0.0555051402## [13,] 0.03881204 -0.0952479065## [14,] -0.03091807 -0.1257612071## [15,] -0.17041473 -0.1418731101## ## , , ori13## ## [,1] [,2]## [1,] -0.58443673 -0.0012178556## [2,] -0.57317082 0.0133383232## [3,] -0.15431669 0.1532975098## [4,] 0.05543398 0.1083234951## [5,] 0.10456713 0.0874340181## [6,] 0.14625152 0.0591346873## [7,] 0.16884067 0.0425453619## [8,] 0.19357927 0.0250379598## [9,] 0.21239415 0.0004893965## [10,] 0.19468126 -0.0212857484## [11,] 0.16334171 -0.0438029480## [12,] 0.12628777 -0.0658700415## [13,] 0.06758279 -0.0961119588## [14,] 0.02782657 -0.1115556496## [15,] -0.14886255 -0.1497565498## ## , , ori14## ## [,1] [,2]## [1,] -0.54915570 -0.007541623## [2,] -0.56264891 0.008110592## [3,] -0.14536324 0.163288099## [4,] -0.03172289 0.157176128## [5,] 0.08323578 0.117393726## [6,] 0.15176586 0.071069519## [7,] 0.18420428 0.041508441## [8,] 0.20667375 0.005985983## [9,] 0.21087451 -0.019214530## [10,] 0.19986681 -0.037860605## [11,] 0.17153174 -0.060002343## [12,] 0.12425727 -0.086864912## [13,] 0.07982351 -0.106328634## [14,] 0.02783601 -0.120577441## [15,] -0.15117878 -0.126142400## ## , , ori15## ## [,1] [,2]## [1,] -0.57282301 -0.0001088834
## [2,] -0.57285547 0.0151448043## [3,] -0.09400025 0.1507580940## [4,] 0.01115300 0.1408212574## [5,] 0.06949771 0.1186078831## [6,] 0.11406922 0.0991167738## [7,] 0.18134286 0.0521817307## [8,] 0.20330337 0.0172576828## [9,] 0.20855654 -0.0036441270## [10,] 0.20036846 -0.0329649475## [11,] 0.17725200 -0.0575902617## [12,] 0.13158308 -0.0914128154## [13,] 0.07266285 -0.1235309692## [14,] -0.03373068 -0.1411792175## [15,] -0.09637969 -0.1434570045## ## , , ori16## ## [,1] [,2]## [1,] -0.58403714 -0.002354455## [2,] -0.58624730 0.013537457## [3,] -0.13521942 0.167516115## [4,] 0.04557850 0.124874294## [5,] 0.09196605 0.098648376## [6,] 0.13140863 0.071499953## [7,] 0.16853772 0.040177975## [8,] 0.18280551 0.016832318## [9,] 0.19804367 -0.003902573## [10,] 0.19483163 -0.027795615## [11,] 0.16154769 -0.060457615## [12,] 0.12123332 -0.081374541## [13,] 0.08815699 -0.100921021## [14,] 0.04795683 -0.116956628## [15,] -0.12656267 -0.139324039
#PCA passo-a-passosup$coords #array
## , , ori1 ## ## [,1] [,2]## [1,] -0.41141968 0.003584539## [2,] -0.41016829 0.026467190## [3,] -0.21769177 0.250135576## [4,] -0.01564311 0.194983654## [5,] 0.03292593 0.167000003## [6,] 0.10739529 0.127992550## [7,] 0.16075954 0.092448512## [8,] 0.20498298 0.058390595## [9,] 0.32084435 0.001126667## [10,] 0.21712019 -0.052791254## [11,] 0.16036732 -0.096743512
## [12,] 0.10127709 -0.132588336## [13,] 0.03676838 -0.180990032## [14,] -0.04945354 -0.216951328## [15,] -0.23806468 -0.242064825## ## , , ori2 ## ## [,1] [,2]## [1,] -0.40143371 -0.006744274## [2,] -0.39944299 0.021374951## [3,] -0.20093338 0.255603082## [4,] -0.06214992 0.229817899## [5,] 0.03777037 0.187077651## [6,] 0.10854744 0.146540412## [7,] 0.17265335 0.105409955## [8,] 0.22824572 0.056596184## [9,] 0.30895168 -0.009433858## [10,] 0.19659395 -0.082100492## [11,] 0.15445189 -0.118131103## [12,] 0.11853256 -0.140342335## [13,] 0.01695268 -0.187333026## [14,] -0.05759739 -0.215750591## [15,] -0.22114224 -0.242584456## ## , , ori3 ## ## [,1] [,2]## [1,] -0.447696463 -0.001780098## [2,] -0.446277897 0.016802720## [3,] -0.242630227 0.246282687## [4,] 0.007855693 0.169094198## [5,] 0.064665979 0.130582339## [6,] 0.106280830 0.096244886## [7,] 0.159560457 0.063799026## [8,] 0.194742426 0.032806576## [9,] 0.296474042 -0.020176662## [10,] 0.198346161 -0.060483320## [11,] 0.161089001 -0.078681424## [12,] 0.121272498 -0.098658631## [13,] 0.077146179 -0.120266880## [14,] 0.040894938 -0.140301347## [15,] -0.291723617 -0.235264069## ## , , ori4 ## ## [,1] [,2]## [1,] -0.42461617 -0.010518138## [2,] -0.42571742 0.020341522## [3,] -0.23865949 0.241182391## [4,] 0.01152129 0.184144309
## [5,] 0.05163125 0.158737537## [6,] 0.09982253 0.127817385## [7,] 0.17638252 0.078717145## [8,] 0.22162288 0.044647729## [9,] 0.30822091 -0.007793855## [10,] 0.21971699 -0.038060211## [11,] 0.15688391 -0.090447431## [12,] 0.09359703 -0.124923778## [13,] 0.01340323 -0.171725978## [14,] -0.03415039 -0.192514912## [15,] -0.22965908 -0.219603717## ## , , ori5 ## ## [,1] [,2]## [1,] -0.400859326 -0.018340000## [2,] -0.401587293 0.004556281## [3,] -0.193439703 0.234257306## [4,] -0.047330713 0.212279019## [5,] 0.008639234 0.193899822## [6,] 0.109555656 0.147611654## [7,] 0.190737098 0.101613849## [8,] 0.250754692 0.051636990## [9,] 0.358484905 -0.003377464## [10,] 0.225426908 -0.067611400## [11,] 0.165184004 -0.102996029## [12,] 0.047987566 -0.162848353## [13,] -0.027741688 -0.185071958## [14,] -0.070063147 -0.196631514## [15,] -0.215748192 -0.208978204## ## , , ori6 ## ## [,1] [,2]## [1,] -0.43001605 0.007508726## [2,] -0.42659477 0.028719032## [3,] -0.17032161 0.244590694## [4,] -0.03247324 0.197172376## [5,] 0.02153886 0.166371843## [6,] 0.08622355 0.120758358## [7,] 0.14513014 0.082110501## [8,] 0.19936750 0.040157379## [9,] 0.29638866 -0.010774668## [10,] 0.22233134 -0.046823086## [11,] 0.18313511 -0.084274950## [12,] 0.12650831 -0.123779754## [13,] 0.07343022 -0.166454845## [14,] -0.03730582 -0.209579465## [15,] -0.25734220 -0.245702143##
## , , ori7 ## ## [,1] [,2]## [1,] -0.42550079 -0.025281875## [2,] -0.42653854 0.005827410## [3,] -0.21518442 0.275583380## [4,] 0.04891699 0.180467923## [5,] 0.08474374 0.163799525## [6,] 0.12437974 0.140611975## [7,] 0.15137943 0.117130550## [8,] 0.19695188 0.081665913## [9,] 0.29473308 -0.001349024## [10,] 0.18084857 -0.070685284## [11,] 0.14134353 -0.109685531## [12,] 0.07870396 -0.149661380## [13,] 0.04992561 -0.164625277## [14,] -0.06170597 -0.204386808## [15,] -0.22299682 -0.239411499## ## , , ori8 ## ## [,1] [,2]## [1,] -0.40217058 -0.018230880## [2,] -0.40164584 0.009784791## [3,] -0.21719529 0.242151571## [4,] -0.03368417 0.216584190## [5,] 0.01669642 0.198498082## [6,] 0.11438269 0.158600099## [7,] 0.18185223 0.103250204## [8,] 0.23175723 0.055194860## [9,] 0.34554301 -0.030296354## [10,] 0.19969767 -0.079873197## [11,] 0.14375026 -0.113032110## [12,] 0.06656938 -0.151974917## [13,] 0.01632866 -0.183527968## [14,] -0.02919172 -0.195888015## [15,] -0.23268995 -0.211240356## ## , , ori9## ## [,1] [,2]## [1,] -0.54219385 0.0001219051## [2,] -0.54411166 0.0100810695## [3,] -0.16517670 0.1342128620## [4,] 0.03831884 0.1118293164## [5,] 0.11280618 0.0951210641## [6,] 0.15223594 0.0764655430## [7,] 0.17333355 0.0609461246## [8,] 0.21496586 0.0410156570## [9,] 0.23330242 0.0207029637
## [10,] 0.22559659 -0.0052883668## [11,] 0.18974033 -0.0371956147## [12,] 0.11469450 -0.0882356142## [13,] 0.02493600 -0.1324049077## [14,] -0.07892433 -0.1416903193## [15,] -0.14952367 -0.1456816827## ## , , ori10## ## [,1] [,2]## [1,] -0.52439805 -0.003567778## [2,] -0.54526133 0.006141455## [3,] -0.16697203 0.159855361## [4,] 0.01337269 0.138921849## [5,] 0.06723178 0.117650950## [6,] 0.11728582 0.090236238## [7,] 0.17405603 0.045665767## [8,] 0.22494438 0.011794143## [9,] 0.24435497 -0.012792621## [10,] 0.22345655 -0.029818900## [11,] 0.16926917 -0.055992343## [12,] 0.13480169 -0.082706524## [13,] 0.04619262 -0.121993659## [14,] -0.01065480 -0.131331612## [15,] -0.16767949 -0.132062326## ## , , ori11## ## [,1] [,2]## [1,] -0.56076011 0.001366836## [2,] -0.55564178 0.015124697## [3,] -0.20288043 0.151688628## [4,] 0.03332742 0.113880041## [5,] 0.09652735 0.084850370## [6,] 0.12818050 0.070604583## [7,] 0.18274750 0.026877883## [8,] 0.20455198 0.009807475## [9,] 0.21819360 -0.013941172## [10,] 0.19050466 -0.033766301## [11,] 0.16820167 -0.043806427## [12,] 0.13627675 -0.062921982## [13,] 0.10902870 -0.084836911## [14,] 0.06005235 -0.105941480## [15,] -0.20831017 -0.128986239## ## , , ori12## ## [,1] [,2]## [1,] -0.56305122 -0.0217057856## [2,] -0.56360392 -0.0102612875
## [3,] -0.16987770 0.1570619056## [4,] 0.08398738 0.1126682554## [5,] 0.12982204 0.0874466215## [6,] 0.16223313 0.0614531403## [7,] 0.18399459 0.0415411011## [8,] 0.20579271 0.0232854551## [9,] 0.21566079 0.0006547272## [10,] 0.19341524 -0.0098659570## [11,] 0.16910922 -0.0238908120## [12,] 0.11503848 -0.0555051402## [13,] 0.03881204 -0.0952479065## [14,] -0.03091807 -0.1257612071## [15,] -0.17041473 -0.1418731101## ## , , ori13## ## [,1] [,2]## [1,] -0.58443673 -0.0012178556## [2,] -0.57317082 0.0133383232## [3,] -0.15431669 0.1532975098## [4,] 0.05543398 0.1083234951## [5,] 0.10456713 0.0874340181## [6,] 0.14625152 0.0591346873## [7,] 0.16884067 0.0425453619## [8,] 0.19357927 0.0250379598## [9,] 0.21239415 0.0004893965## [10,] 0.19468126 -0.0212857484## [11,] 0.16334171 -0.0438029480## [12,] 0.12628777 -0.0658700415## [13,] 0.06758279 -0.0961119588## [14,] 0.02782657 -0.1115556496## [15,] -0.14886255 -0.1497565498## ## , , ori14## ## [,1] [,2]## [1,] -0.54915570 -0.007541623## [2,] -0.56264891 0.008110592## [3,] -0.14536324 0.163288099## [4,] -0.03172289 0.157176128## [5,] 0.08323578 0.117393726## [6,] 0.15176586 0.071069519## [7,] 0.18420428 0.041508441## [8,] 0.20667375 0.005985983## [9,] 0.21087451 -0.019214530## [10,] 0.19986681 -0.037860605## [11,] 0.17153174 -0.060002343## [12,] 0.12425727 -0.086864912## [13,] 0.07982351 -0.106328634## [14,] 0.02783601 -0.120577441
## [15,] -0.15117878 -0.126142400## ## , , ori15## ## [,1] [,2]## [1,] -0.57282301 -0.0001088834## [2,] -0.57285547 0.0151448043## [3,] -0.09400025 0.1507580940## [4,] 0.01115300 0.1408212574## [5,] 0.06949771 0.1186078831## [6,] 0.11406922 0.0991167738## [7,] 0.18134286 0.0521817307## [8,] 0.20330337 0.0172576828## [9,] 0.20855654 -0.0036441270## [10,] 0.20036846 -0.0329649475## [11,] 0.17725200 -0.0575902617## [12,] 0.13158308 -0.0914128154## [13,] 0.07266285 -0.1235309692## [14,] -0.03373068 -0.1411792175## [15,] -0.09637969 -0.1434570045## ## , , ori16## ## [,1] [,2]## [1,] -0.58403714 -0.002354455## [2,] -0.58624730 0.013537457## [3,] -0.13521942 0.167516115## [4,] 0.04557850 0.124874294## [5,] 0.09196605 0.098648376## [6,] 0.13140863 0.071499953## [7,] 0.16853772 0.040177975## [8,] 0.18280551 0.016832318## [9,] 0.19804367 -0.003902573## [10,] 0.19483163 -0.027795615## [11,] 0.16154769 -0.060457615## [12,] 0.12123332 -0.081374541## [13,] 0.08815699 -0.100921021## [14,] 0.04795683 -0.116956628## [15,] -0.12656267 -0.139324039
tudo1 <- two.d.array(sup$coords)tudo1 <- scale(tudo1, center = TRUE, scale = FALSE)
p1 <- dim(tudo1)[2]Nspec <- dim(tudo1)[1]uns <- rep(1,dim(tudo1)[1]) #calculando a matriz de variância-covariância...W <- t(tudo1) %*% tudo1 * (Nspec - 1)^-1 #para extrair autovetores X = ZLZ'
eigC <- eigen(W) #e1=t(e11,e12) é o primeiro autovetor dos escores quadrados do poolednames(eigC)
## [1] "values" "vectors"
eigC$values #auto-valores
## [1] 3.464151e-02 3.663080e-03 2.252777e-03 1.323078e-03 9.731533e-04## [6] 3.584560e-04 2.084231e-04 1.725651e-04 1.557645e-04 9.748341e-05## [11] 6.930297e-05 4.753272e-05 2.022588e-05 1.579210e-05 3.829458e-06## [16] 3.358079e-18 4.636635e-19 1.182878e-19 1.145270e-19 6.209600e-20## [21] 5.260590e-20 7.202755e-21 -9.034175e-21 -3.897160e-20 -3.908484e-20## [26] -6.165754e-20 -2.368804e-19 -2.444947e-19 -2.670260e-19 -4.575341e-19
eigC$vectors #auto-vetores
## [,1] [,2] [,3] [,4] [,5]## [1,] 0.40488009 -0.056706955 -0.038845174 0.08327025 0.0689271004## [2,] -0.01418739 -0.033382357 0.089189077 -0.05891293 0.2069996498## [3,] 0.41037242 -0.086934008 -0.069861947 0.03436321 0.0675524298## [4,] 0.01899345 -0.039706456 0.083957362 -0.09971180 0.1289228187## [5,] -0.14925843 0.350044182 0.276947922 -0.33681294 0.0456491072## [6,] 0.25075905 -0.187203270 -0.039935010 -0.27330286 -0.1927684687## [7,] -0.15115595 -0.130880326 -0.571808335 -0.15951813 -0.1866647796## [8,] 0.21115995 0.059783015 0.233857955 -0.03362681 -0.0864592372## [9,] -0.16362081 -0.072813208 -0.354017785 -0.08442858 -0.1030347872## [10,] 0.20802653 0.121507290 0.148702068 -0.01316374 -0.1381437795## [11,] -0.08302182 0.055443291 -0.162901644 0.09941255 -0.1699789642## [12,] 0.17408604 0.112296272 0.050989273 -0.04964530 -0.1602204749## [13,] -0.01923776 0.087879147 0.039548946 0.24459844 -0.1097492900
## [14,] 0.14393410 0.097320929 -0.091940955 -0.14006229 -0.1360410834## [15,] 0.04789817 0.143746669 0.024714164 0.30616881 0.0118536931## [16,] 0.09558421 0.041456506 -0.191845814 -0.14373873 -0.1025411147## [17,] 0.28428621 0.007760075 -0.040405244 0.28247801 -0.0005612274## [18,] -0.01643140 0.082465995 -0.148333488 -0.07625128 0.1162183182## [19,] 0.02009127 0.090866438 0.019026271 0.13677966 0.3209202722## [20,] -0.10719246 0.042002577 -0.138792145 0.03795526 0.2670638421## [21,] -0.03442075 0.052727965 0.031435912 0.01116872 0.3050043242## [22,] -0.14785321 -0.013715314 -0.113529068 0.11371231 0.2429624877## [23,] -0.09464470 -0.123653271 0.143375227 -0.19701619 0.3486334340## [24,] -0.17452653 -0.131958405 -0.038647487 0.06207190 0.1880838175## [25,] -0.11726624 -0.325433983 0.228368620 -0.37537471 0.0107684806## [26,] -0.18852322 -0.184354529 0.002114677 0.06472592 -0.0629213489## [27,] -0.13544358 -0.493779946 0.374545629 0.13868954 -0.3240817273## [28,] -0.21075889 -0.132196821 0.053111044 0.25671919 -0.1267408898## [29,] -0.21945812 0.501733930 0.099877440 -0.18377863 -0.2852380658## [30,] -0.24307023 0.165684567 0.101102511 0.35323115 -0.1444145368## [,6] [,7] [,8] [,9] [,10]## [1,] -0.099742562 -0.070133651 -0.06307489 0.043436133 -0.21852247## [2,] 0.078855682 -0.117718918 0.11883920 -0.216113104 0.14998037## [3,] -0.040656972 0.007632397 0.03914277 -0.050083760 0.13712260## [4,] 0.077434534 -0.206273686 0.16351557 -0.204626337 0.07614175## [5,] 0.135663114 0.509801959 -0.06972745 0.204002311 0.09704644## [6,] 0.003332952 0.093368170 0.16814755 0.275413557 -0.25806494## [7,] 0.445016538 -0.099151204 -0.16649310 0.258917810 -0.02902268
## [8,] -0.223095608 0.043181723 0.08624612 0.249544353 -0.16818167## [9,] -0.423725579 -0.047554891 0.05638115 -0.046390481 -0.01430362## [10,] 0.028037967 0.043624954 -0.08998096 0.115909488 -0.13699109## [11,] -0.419633069 0.285109705 0.16704007 -0.224068825 -0.17282038## [12,] 0.107458593 -0.247938102 -0.34247846 0.028993466 0.14275909## [13,] -0.081396863 -0.071587656 -0.02734369 0.129760326 0.06922712## [14,] -0.075475689 0.057321007 -0.05407390 -0.169477568 0.15101843## [15,] -0.080698589 -0.124294998 -0.15337365 0.128920143 0.14703692## [16,] -0.035336910 -0.001478248 0.02199271 -0.291812371 0.16907084## [17,] 0.292996493 0.175372457 -0.01958293 -0.078074730 0.24009585## [18,] 0.033863978 0.005061871 0.22363947 -0.223187856 0.12205524## [19,] 0.239227213 -0.029865510 0.13609524 -0.101483758 -0.27377826## [20,] 0.167067450 -0.026890197 0.17529956 0.010568590 -0.40143342## [21,] 0.007209828 0.204403640 -0.05694205 -0.119146597 -0.01260869## [22,] 0.022687191 0.203796804 -0.08829248 0.104186584 -0.04717980## [23,] -0.276755832 -0.384278453 -0.02246889 0.269295563 0.22956465## [24,] -0.109283641 -0.063953589 0.05146311 0.346697754 0.07920413## [25,] -0.006889690 0.007342937 -0.47591763 -0.350938069 -0.16169869## [26,] -0.056337749 0.244970509 -0.09619293 0.124401271 0.11680819## [27,] 0.216406414 -0.049491451 0.35928358 -0.050945148 -0.05148434## [28,] 0.020264261 0.158229879 0.02734123 -0.006470536 0.34905530## [29,] 0.092979554 -0.313305281 0.29698147 -0.013200918 0.01414555## [30,] -0.039473010 -0.185302176 -0.36546577 -0.144027291 -0.34424242## [,11] [,12] [,13] [,14] [,15]## [1,] -0.268005169 0.06569718 0.03780762 0.20376944 -0.156681071## [2,] 0.059641980 0.07686793 -0.01370296 0.14754561 -0.189938866## [3,] 0.259462647 -0.13766743 -0.02525117 -0.21881255 0.153089827
## [4,] 0.145894734 -0.08471355 0.10034683 -0.11457754 0.234806674## [5,] 0.004446838 0.09980246 -0.12150962 -0.19651183 -0.087212998## [6,] -0.270207094 -0.17555432 -0.17654274 0.19771027 0.258104535## [7,] 0.063927773 0.11272685 -0.02641215 -0.05699347 -0.180111118## [8,] 0.080096399 -0.05561304 0.08980201 -0.01130027 -0.359734462## [9,] -0.173471270 -0.18475376 0.15715082 -0.22631216 -0.103615183## [10,] 0.077000497 0.16050991 0.13948462 -0.15006588 0.094181323## [11,] 0.224964617 0.35624608 0.04699580 0.12283805 0.007410994## [12,] 0.044291840 -0.07733175 0.19770541 -0.12494213 -0.260838234## [13,] 0.317683467 -0.48577414 0.05427351 0.22423427 -0.072266328## [14,] -0.112680128 0.18922193 0.02268359 -0.15908528 0.094261833## [15,] -0.087521461 -0.06169296 -0.32614438 -0.32043905 0.416986774## [16,] 0.051169579 0.16247297 -0.07537188 -0.10353008 0.021452263## [17,] 0.063101238 0.22444031 0.03880331 0.36556300 0.051764517## [18,] -0.058212772 -0.23431649 -0.53709040 0.11709338 -0.284425321## [19,] -0.344646276 0.09990773 0.04931204 0.01557186 -0.006486131## [20,] 0.123214892 -0.06753812 0.23522309 -0.21319368 0.203375948## [21,] -0.088608474 -0.29558409 0.08619021 -0.16976266 -0.247375563## [22,] 0.216459261 -0.03451242 0.09136680 0.07852738 0.115104640## [23,] -0.138117736 0.30370737 -0.06187289 0.03134956 0.004932905## [24,] 0.289840078 0.20445255 -0.00598147 0.16005901 -0.039912922## [25,] 0.095398030 -0.11575594 0.07656770 0.23151471 0.176955250## [26,] -0.117795122 -0.14615254 -0.21378928 0.15858709 0.211341161## [27,] 0.093426988 0.08988500 -0.12067554 -0.29180808 -0.150447403## [28,] -0.449967451 -0.05529785 0.44016405 0.02902571 0.009767763## [29,] -0.022041211 -0.07118467 0.13476476 0.28579891 0.193055527## [30,] -0.078746691 0.13750481 -0.29429768 -0.01185358 -0.107546335## [,16] [,17] [,18] [,19] [,20]## [1,] -0.647006386 0.0000000000 0.000000000 0.000000000 0.0000000000## [2,] -0.428201573 -0.0989711187 -0.384171298 0.015324913 0.0097692285## [3,] 0.043781058 0.1917066829 -0.223259016 0.047391258 0.0074984493## [4,] -0.077023282 -0.2150526596 -0.020806908 0.205361752 0.0755044038## [5,] -0.167230649 0.0061824931 -0.249660219 0.124928969 -0.1079061214## [6,] 0.162888921 -0.1970894892 -0.348764454 0.030080966 -0.0594811083## [7,] -0.096663765 0.0997780973 -0.072883502 0.093127766 0.1707519328## [8,] 0.159531943 -0.0667033966 0.020515312 -0.352687403 0.1274455468## [9,] -0.036929799 -0.0863570959 -0.002457848 -0.057165397 -0.3185331775## [10,] -0.132602645 -0.0827110496 0.449528441 0.422970594 0.1022061851## [11,] 0.057165536 -0.1128237011 -0.218874393 0.237125695
0.3096437684## [12,] 0.150474528 -0.5256484353 -0.158336466 0.001976348 0.1451219059## [13,] -0.064308573 0.0055064656 -0.102407431 0.275972065 0.0252998745## [14,] 0.012711690 -0.1497186125 -0.180183855 -0.157610933 0.0642933080## [15,] -0.138083781 -0.0002190085 -0.166889220 -0.094145442 -0.0002667323## [16,] -0.112537926 -0.0940491692 0.220537019 -0.267410538 -0.0784259441## [17,] 0.222961461 -0.0228121164 -0.042741155 -0.239724636 0.0065234111## [18,] 0.121117954 -0.1740888993 0.086410240 0.222824472 0.1147291828## [19,] 0.226337370 -0.1326618683 0.054668168 0.156801866 -0.1585044224## [20,] -0.033018050 -0.0601372023 -0.174046267 -0.178547805 0.3839673154## [21,] -0.011524542 0.1276327161 0.026944878 -0.246436945 0.2526803684## [22,] -0.096190525 -0.5890368693 0.078678335 -0.091241078 -0.3704212716## [23,] 0.148292205 -0.0839248627 -0.001877818 0.088547837 0.2448497937## [24,] -0.033561422 0.0919977059 -0.092685565 -0.115618839 -0.1707558904## [25,] 0.037764636 0.0984800757 -0.055431030 -0.021326019 -0.0275487433## [26,] -0.204164742 -0.2422220383 0.275787748 -0.188681523 0.4544250846## [27,] -0.103708205 -0.1357890199 -0.004976347 -0.089105363 -0.0609342827## [28,] 0.005094909 0.0286448818 -0.185947528 0.180998286 0.0789016677## [29,] -0.122959936 0.0250817865 0.036563707 -0.232152347 0.0154542849## [30,] 0.042240569 -0.0151686435 -0.211613871 -0.038661541 -0.0206640797## [,21] [,22] [,23] [,24] [,25]## [1,] 0.00000000 0.000000000 0.00000000 0.000000000 0.000000000## [2,] 0.02267396 0.065595060 -0.06887712 0.024418202 0.024493159## [3,] 0.35842798 0.156313757 -0.10131355 0.180561074 -0.085044257## [4,] -0.22661268 0.053726429 0.71382206 0.124425817 -0.086352110## [5,] -0.10578527 0.058192535 -0.04250427 0.224796122 -
0.153417923## [6,] -0.23696766 -0.210275214 0.05113261 -0.045186344 0.036050797## [7,] 0.11282552 -0.122929288 0.13369970 -0.047503402 -0.116539160## [8,] 0.08664143 0.134438509 0.20709400 -0.110538361 -0.114145766## [9,] -0.20323206 0.250716658 -0.06671007 0.238942660 -0.202569692## [10,] -0.22978685 0.098145424 -0.10342831 -0.252611322 -0.090998960## [11,] 0.14056447 -0.246745505 0.03153924 0.038072551 0.098939894## [12,] 0.06394638 -0.006700943 -0.07684469 0.130357339 0.194440663## [13,] -0.09124236 -0.237465076 -0.16999901 -0.005190994 -0.503321525## [14,] 0.16167757 0.167756082 0.05721596 -0.504258843 -0.432384492## [15,] 0.01359628 -0.169334585 -0.02721116 -0.194479603 0.090215676## [16,] -0.26085306 -0.377935293 -0.13719799 0.087861450 -0.214212451## [17,] -0.36548220 0.116791717 -0.05232555 0.155744029 -0.136164592## [18,] -0.09246425 0.259959643 -0.12820886 -0.307176914 0.085858960## [19,] 0.36700115 -0.115660407 0.01391800 0.099017150 -0.432860446## [20,] -0.26458392 0.249126652 -0.35220520 -0.031775999 -0.015402217## [21,] -0.11809082 -0.455149573 0.17813028 -0.177836862 -0.002511722## [22,] 0.14104351 -0.112534853 -0.06420203 -0.161952582 0.137791064## [23,] -0.08596484 -0.174441711 -0.22515345 0.106843551 -0.148018808## [24,] -0.08961664 0.138774967 0.19373509 -0.304401555 -0.125947409## [25,] 0.03862177 0.036809317 -0.12052071 -0.167265983 -0.099459467## [26,] 0.21452647 0.202750719 0.09161687 0.274025843 -0.186825095## [27,] 0.02324619 -0.111910469 -0.14931278 -0.025788060 -0.097737212## [28,] -0.06449251 0.058255011 -0.01235708 -0.202522922 0.063508675## [29,] 0.16821020 -0.039993819 -0.05773041 -0.041776538 0.013241345## [30,] -0.18667059 0.109428009 0.14242291 0.084984917 -
0.114879089## [,26] [,27] [,28] [,29] [,30]## [1,] 0.0000000000 0.000000000 0.00000000 0.000000000 0.434646494## [2,] -0.0151494767 -0.087292057 -0.06440126 0.002249824 -0.640065213## [3,] -0.3807991556 0.342047417 -0.12524705 -0.235551135 0.060307811## [4,] -0.0873367516 -0.089903395 0.05954565 0.005171620 0.167972097## [5,] -0.0515976740 -0.025128668 -0.03111468 0.045430119 0.208402467## [6,] -0.0120472037 0.188116478 -0.04111048 -0.043908662 -0.177580079## [7,] -0.2138119198 -0.195317354 -0.03761393 -0.082655485 -0.003138224## [8,] -0.4228369799 -0.308720473 0.09223608 0.169283868 -0.125971480## [9,] 0.0232086789 -0.177851723 -0.33130383 -0.152384390 -0.034424831## [10,] -0.1281039006 0.075735685 -0.27409785 -0.159242414 -0.302251136## [11,] -0.0081813159 -0.101307009 -0.18551776 0.034497836 0.098331870## [12,] 0.1961299802 0.165979794 -0.24137053 0.196660202 0.106135938## [13,] 0.1084340073 -0.069865787 0.17223885 0.058577577 0.028788348## [14,] 0.3163595324 0.024117701 0.23849342 -0.188944280 0.023185154## [15,] -0.0815985067 -0.392854675 -0.26211075 0.208243326 -0.005260633## [16,] -0.2991681266 0.264201370 0.12681215 0.388882157 -0.045670761## [17,] -0.0016377334 -0.249505304 -0.22101745 -0.211840474 0.080544153## [18,] -0.1787017637 -0.005243472 -0.09747678 0.046838088 0.202807612## [19,] -0.0238436017 -0.020279224 -0.23345558 0.226885667 -0.044548839## [20,] 0.0001201096 0.021809440 0.10468847 0.145096664 0.089696547## [21,] 0.0681550829 0.142910437 -0.29520902 -0.333084024 -0.021011955## [22,] -0.2398645672 -0.027378360 0.16300919 -0.278003908 0.048852497## [23,] -0.1294184598 -0.062557119 0.09293757 -0.262317454 0.109166990## [24,] 0.0935569140 0.383200984 -0.37129643 0.279688282
0.086378448## [25,] -0.1692599077 -0.178282538 -0.20605490 0.096724675 0.122834743## [26,] 0.0555383859 0.137037125 -0.08107903 0.041443312 -0.125763603## [27,] 0.0495271653 -0.035545418 -0.11052551 -0.131310951 0.175774842## [28,] -0.3687414731 0.136052996 0.07044094 0.124023853 0.055143802## [29,] -0.1433501489 0.064420960 -0.23049523 -0.196093395 0.119583655## [30,] -0.2131730644 0.288895422 0.10850635 -0.214044117 -0.052439431
W.PCA <- tudo1 %*% eigC$vectorsW.PCA
## [,1] [,2] [,3] [,4] [,5]## ori1 0.1895084 -0.008475479 -0.010911506 -0.019201445 0.0264719242## ori2 0.2237445 0.028091198 0.032843806 -0.020722220 0.0012638330## ori3 0.0773003 -0.147147392 0.001610027 0.013271939 0.0095620620## ori4 0.1454586 -0.013737621 -0.033859511 0.021597118 0.0081642541## ori5 0.2306528 0.082501139 0.009760373 0.061472557 -0.0126565857## ori6 0.1498341 -0.026994316 0.041335902 -0.050647211 0.0652660945## ori7 0.1594289 -0.013234948 -0.080007386 -0.064923769 -0.0543545623## ori8 0.2247964 0.015636288 0.024457007 0.036595301 -0.0443726919## ori9 -0.1394226 0.077114809 -0.073691712 0.014129798 0.0464100580## ori10 -0.1119244 0.021696813 0.019888208 0.033250338 0.0194586604## ori11 -0.1899225 -0.094726866 0.017949952 0.033528006 -0.0003500213## ori12 -0.1958702 0.005804825 -0.086777440 0.016876495 0.0014797489## ori13 -0.2158584 -0.017407854 -0.015065040 -0.007650363 -0.0120903990## ori14 -0.1580013 0.008520283 0.074021734 0.014765829 -0.0166098059## ori15 -0.1724035 0.091666778 0.048709684 -0.049117687 0.0002608463## ori16 -0.2173211 -0.009307657 0.029735901 -0.033224687 -0.0379034152
## [,6] [,7] [,8] [,9] [,10]## ori1 0.0064864277 -0.0076540826 0.011245327 -0.011637913 -0.0064323486## ori2 -0.0438262424 -0.0162116469 0.010888042 0.010277521 0.0135445265## ori3 -0.0005016489 0.0136689213 0.005739281 0.005127099 0.0129637128## ori4 0.0162178868 -0.0272183561 0.013424601 0.010427528 -0.0128373740## ori5 0.0183260699 0.0228124553 0.003987849 -0.002174177 0.0048805354## ori6 0.0112218566 0.0188953317 -0.010446545 0.002292269 -0.0082246246## ori7 -0.0058475267 0.0013505936 -0.015469410 -0.007412914 -0.0039025486## ori8 0.0060289024 -0.0002194179 -0.013542223 -0.003937023 0.0007331612## ori9 -0.0114168519 -0.0010598759 0.001526563 -0.024789324 0.0045277034## ori10 0.0091416373 -0.0177726132 -0.012630977 0.013047510 -0.0030235072## ori11 -0.0029020461 -0.0147049142 -0.021554169 -0.014330151 0.0042944608## ori12 -0.0149362380 0.0163302608 -0.004700804 0.027122764 -0.0059833588## ori13 0.0107537782 0.0054260050 0.020866478 -0.002808656 0.0130922412## ori14 -0.0361724468 0.0122083311 0.006318757 -0.007728250 -0.0188419805## ori15 0.0137861240 -0.0040321469 -0.012813810 0.008976145 0.0119174259## ori16 0.0236403181 -0.0018188451 0.017161041 -0.002452428 -0.0067080249## [,11] [,12] [,13] [,14] [,15]## ori1 0.0100673698 4.550590e-03 -0.003206087 0.0105943374 -2.449973e-04## ori2 0.0010203616 1.747189e-04 -0.003740661 -0.0029324428 -1.353724e-03## ori3 -0.0110427432 -2.766625e-03 0.006081245 0.0035618775 -9.129857e-04## ori4 0.0005441149 -1.007647e-02 0.004506574 -0.0035179769 1.772980e-03## ori5 -0.0045860471 -7.979963e-03 -0.006583921 0.0001256150 2.594855e-04## ori6 0.0029151064 2.332872e-03 -0.001094729 -0.0061631471 2.402064e-04## ori7 -0.0099281988 -6.227065e-04 -0.002138003 -0.0001232305 1.464972e-03
## ori8 0.0113415326 1.095396e-02 0.007845276 -0.0019045221 -1.095682e-03## ori9 -0.0051483491 1.933386e-04 0.004810561 -0.0022507812 -1.657064e-03## ori10 -0.0166223754 1.294162e-02 -0.003295872 0.0018424940 4.363207e-04## ori11 0.0088878929 -7.705274e-03 -0.006050157 -0.0013710826 -3.854916e-05## ori12 0.0105695469 2.996394e-05 -0.001208989 0.0013786400 -1.328699e-03## ori13 0.0060016552 9.059047e-03 -0.001515489 -0.0030772142 4.189817e-03## ori14 -0.0037212037 -2.157816e-03 0.002618453 0.0016833121 1.960195e-03## ori15 0.0025666844 -8.941255e-03 0.005058080 0.0044291080 9.092244e-04## ori16 -0.0028653472 1.399944e-05 -0.002086282 -0.0022749867 -4.601500e-03## [,16] [,17] [,18] [,19]## ori1 7.407269e-16 2.428613e-17 1.509209e-16 1.084202e-17## ori2 -4.592680e-16 -1.626303e-17 -2.324529e-16 2.168404e-17## ori3 -1.864828e-17 -1.271769e-16 -3.330669e-16 -1.647987e-17## ori4 -8.500145e-17 -2.081668e-17 2.367898e-16 -3.404395e-17## ori5 7.415943e-17 8.933826e-17 1.543904e-16 -4.054916e-17## ori6 -3.660267e-16 5.410169e-17 9.887924e-17 -2.168404e-18## ori7 9.801188e-17 8.651933e-17 2.185752e-16 -7.329207e-17## ori8 -4.657733e-16 -1.282069e-16 -2.046974e-16 5.854692e-18## ori9 -2.226951e-16 -1.821460e-16 -3.486794e-16 3.230922e-17## ori10 4.185020e-16 6.364267e-17 7.806256e-17 -3.122502e-17## ori11 -8.500145e-17 6.082374e-17 1.405126e-16 1.214306e-17## ori12 7.285839e-17 3.805550e-17 -1.543904e-16 4.466913e-17## ori13 8.456777e-17 1.086371e-16 7.650131e-16 -6.960578e-17## ori14 4.033232e-16 5.009014e-17 2.532696e-16 -2.688821e-17## ori15 2.667137e-16 -2.558717e-17 1.630640e-16 -5.789640e-17## ori16 -3.144186e-16 -2.110942e-16 -7.389922e-16 6.722053e-17## [,20] [,21] [,22] [,23]## ori1 1.309716e-16 2.185752e-16 3.816392e-17 -8.500145e-17## ori2 5.204170e-18 -2.602085e-17 3.729655e-17 -5.724587e-17## ori3 -1.095044e-16 -7.979728e-17 -9.540979e-18 -7.025630e-17## ori4 3.686287e-18 -7.719519e-17 -2.168404e-18 1.578598e-16## ori5 7.892992e-17 1.734723e-16 -9.974660e-18 -1.257675e-17## ori6 7.155734e-18 -5.030698e-17 1.127570e-17 4.510281e-17## ori7 3.014082e-17 9.540979e-17 -2.602085e-18 3.122502e-17## ori8 -1.440905e-16 -3.061787e-16 2.038300e-17 -6.938894e-18## ori9 -1.349832e-16 -2.194425e-16 8.673617e-18 -4.510281e-17## ori10 -9.974660e-18 9.540979e-17 -1.647987e-17 -1.014813e-16## ori11 9.562663e-17 9.194034e-17 6.938894e-17 3.642919e-17## ori12 5.854692e-18 9.540979e-17 2.341877e-17 -8.586881e-17## ori13 9.356665e-17 -1.301043e-17 -7.936360e-17 2.888315e-16## ori14 4.358493e-17 1.613293e-16 -2.168404e-17 5.898060e-17
## ori15 -1.084202e-19 -4.250073e-17 -1.387779e-17 6.765422e-17## ori16 -1.277190e-16 -1.231654e-16 3.903128e-17 -2.185752e-16## [,24] [,25] [,26] [,27]## ori1 -2.428613e-17 4.597017e-17 2.428613e-17 -2.359224e-16## ori2 -2.602085e-18 2.341877e-17 4.683753e-17 -1.942890e-16## ori3 2.602085e-17 6.938894e-17 -1.214306e-17 -1.231654e-16## ori4 1.040834e-16 -6.158268e-17 -1.023487e-16 3.174544e-16## ori5 5.421011e-17 8.239937e-18 -3.035766e-17 7.806256e-17## ori6 -1.301043e-17 -4.597017e-17 3.469447e-17 9.714451e-17## ori7 4.336809e-17 -2.428613e-17 -5.724587e-17 2.498002e-16## ori8 -1.687019e-16 2.168404e-18 1.214306e-16 -2.125036e-16## ori9 -1.101549e-16 4.423545e-17 1.249001e-16 -3.070461e-16## ori10 -2.515349e-17 3.035766e-17 -5.204170e-18 1.734723e-17## ori11 2.949030e-17 -2.255141e-17 4.510281e-17 -5.204170e-17## ori12 -2.341877e-17 4.250073e-17 4.510281e-17 -1.301043e-16## ori13 1.409463e-16 -1.040834e-16 -1.717376e-16 5.308254e-16## ori14 3.035766e-17 -1.387779e-17 -1.179612e-16 3.226586e-16## ori15 9.974660e-17 2.862294e-17 -5.898060e-17 1.318390e-16## ori16 -1.647987e-16 7.632783e-17 2.046974e-16 -7.372575e-16## [,28] [,29] [,30]## ori1 -9.974660e-17 8.847090e-17 -9.757820e-17## ori2 3.209238e-17 -1.214306e-17 -3.903128e-16## ori3 -2.341877e-17 1.006140e-16 -3.048777e-16## ori4 1.040834e-16 -8.413409e-17 6.114900e-16## ori5 2.818926e-17 -1.474515e-17 1.971080e-16## ori6 5.464379e-17 -4.683753e-17 1.196959e-16## ori7 -7.806256e-18 -1.214306e-17 4.965646e-16## ori8 -1.821460e-17 1.214306e-17 -3.946496e-16## ori9 -3.469447e-18 4.510281e-17 -5.355959e-16## ori10 -1.647987e-17 5.030698e-17 6.505213e-18## ori11 -2.428613e-17 -3.469447e-17 -1.474515e-17## ori12 -2.602085e-18 2.255141e-17 -3.560520e-16## ori13 3.079134e-17 -8.500145e-17 9.892261e-16## ori14 8.673617e-18 -2.602085e-17 5.100087e-16## ori15 -4.597017e-17 5.551115e-17 2.745200e-16## ori16 1.127570e-17 1.561251e-17 -1.222546e-15
Quantidade de variância em cada eixo:#The proportion of the total sum of squares accounted for by the first principal component: TSS <- 0for (i in 1:dim(W.PCA)[2]){ TSS[i] <- round((100 * eigC$values[i] / sum(eigC$values)), 4)}TSS # em porcentagem
## [1] 78.7254 8.3246 5.1196 3.0068 2.2116 0.8146 0.4737 0.3922## [9] 0.3540 0.2215 0.1575 0.1080 0.0460 0.0359 0.0087 0.0000
## [17] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000## [25] 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
#fazendo o histograma:PCs <- c(seq(1:dim(W.PCA)[2]))barplot(TSS[1:dim(W.PCA)[2]], names.arg = PCs, main = 'Variação', xlab = 'Componentes principais', ylab = '% Variância', col = 'yellow')
# criando o fator tipo de folhatudo1 <- readland.tps(file = '~/Dropbox/aulas/Morfogeo/morfo_aulas/alunos_landmark/folhasok.TPS', specID = 'ID')
## ## No curves detected; all points appear to be fixed landmarks.## ## Warning: not all specimens have scale adjustment (perhaps because they are already scaled);## no rescaling will be performed in these cases
tudo1 #um array
## , , ori1 ## ## [,1] [,2]## [1,] 497 1068## [2,] 499 1146## [3,] 1121 1927## [4,] 1813 1760## [5,] 1980 1670## [6,] 2238 1545## [7,] 2423 1430## [8,] 2577 1319## [9,] 2980 1136## [10,] 2631 941## [11,] 2442 785## [12,] 2245 657## [13,] 2031 485## [14,] 1741 353## [15,] 1103 248## ## , , ori2 ## ## [,1] [,2]## [1,] 905 940## [2,] 912 1016## [3,] 1448 1638## [4,] 1815 1563## [5,] 2084 1442## [6,] 2273 1329## [7,] 2444 1215## [8,] 2592 1080## [9,] 2807 897## [10,] 2498 705## [11,] 2383 610## [12,] 2287 553## [13,] 2009 431## [14,] 1807 358## [15,] 1368 294## ## , , ori3 ## ## [,1] [,2]## [1,] 833 942## [2,] 834 991## [3,] 1330 1626## [4,] 2002 1460## [5,] 2157 1367## [6,] 2271 1283## [7,] 2416 1206## [8,] 2513 1130## [9,] 2790 1006
## [10,] 2537 885## [11,] 2442 832## [12,] 2341 774## [13,] 2229 711## [14,] 2138 653## [15,] 1273 350## ## , , ori4 ## ## [,1] [,2]## [1,] 636 963## [2,] 634 1062## [3,] 1237 1759## [4,] 2035 1564## [5,] 2161 1481## [6,] 2313 1380## [7,] 2556 1219## [8,] 2699 1108## [9,] 2974 936## [10,] 2689 844## [11,] 2485 679## [12,] 2281 572## [13,] 2022 426## [14,] 1870 362## [15,] 1244 285## ## , , ori5 ## ## [,1] [,2]## [1,] 631 892## [2,] 631 957## [3,] 1229 1591## [4,] 1635 1518## [5,] 1791 1462## [6,] 2076 1321## [7,] 2304 1183## [8,] 2471 1035## [9,] 2775 869## [10,] 2387 697## [11,] 2212 602## [12,] 1870 441## [13,] 1653 386## [14,] 1535 358## [15,] 1126 337## ## , , ori6 ## ## [,1] [,2]## [1,] 543 1067## [2,] 555 1131
## [3,] 1342 1768## [4,] 1753 1615## [5,] 1914 1518## [6,] 2107 1375## [7,] 2283 1254## [8,] 2445 1123## [9,] 2737 962## [10,] 2510 858## [11,] 2389 747## [12,] 2215 631## [13,] 2052 505## [14,] 1712 381## [15,] 1042 286## ## , , ori7 ## ## [,1] [,2]## [1,] 834 945## [2,] 840 1031## [3,] 1489 1714## [4,] 2188 1376## [5,] 2280 1321## [6,] 2381 1247## [7,] 2447 1176## [8,] 2562 1066## [9,] 2808 809## [10,] 2474 650## [11,] 2355 554## [12,] 2172 462## [13,] 2091 430## [14,] 1772 352## [15,] 1322 301## ## , , ori8 ## ## [,1] [,2]## [1,] 553 943## [2,] 555 1026## [3,] 1089 1710## [4,] 1627 1634## [5,] 1774 1581## [6,] 2064 1462## [7,] 2263 1297## [8,] 2410 1154## [9,] 2748 898## [10,] 2312 753## [11,] 2146 656## [12,] 1917 542## [13,] 1770 450## [14,] 1638 415
## [15,] 1038 373## ## , , ori9## ## [,1] [,2]## [1,] 494 1040## [2,] 490 1068## [3,] 1584 1359## [4,] 2157 1266## [5,] 2366 1208## [6,] 2474 1150## [7,] 2530 1104## [8,] 2645 1042## [9,] 2692 983## [10,] 2669 911## [11,] 2563 826## [12,] 2342 692## [13,] 2080 580## [14,] 1783 570## [15,] 1588 570## ## , , ori10## ## [,1] [,2]## [1,] 661 820## [2,] 613 843## [3,] 1491 1181## [4,] 1905 1126## [5,] 2028 1075## [6,] 2142 1010## [7,] 2271 905## [8,] 2387 825## [9,] 2430 768## [10,] 2382 730## [11,] 2256 672## [12,] 2176 612## [13,] 1970 525## [14,] 1839 506## [15,] 1478 511## ## , , ori11## ## [,1] [,2]## [1,] 379 1058## [2,] 394 1094## [3,] 1348 1431## [4,] 1979 1314## [5,] 2146 1232## [6,] 2228 1193## [7,] 2371 1072
## [8,] 2427 1026## [9,] 2459 963## [10,] 2386 913## [11,] 2327 889## [12,] 2242 841## [13,] 2170 785## [14,] 2039 732## [15,] 1315 689## ## , , ori12## ## [,1] [,2]## [1,] 548 1018## [2,] 548 1046## [3,] 1551 1413## [4,] 2180 1272## [5,] 2290 1204## [6,] 2366 1136## [7,] 2416 1085## [8,] 2467 1038## [9,] 2486 982## [10,] 2432 960## [11,] 2371 929## [12,] 2233 857## [13,] 2038 767## [14,] 1861 699## [15,] 1515 676## ## , , ori13## ## [,1] [,2]## [1,] 688 741## [2,] 711 770## [3,] 1553 1052## [4,] 1974 964## [5,] 2072 923## [6,] 2155 867## [7,] 2199 835## [8,] 2248 801## [9,] 2284 753## [10,] 2251 710## [11,] 2189 665## [12,] 2116 621## [13,] 1999 560## [14,] 1921 529## [15,] 1568 450## ## , , ori14## ## [,1] [,2]
## [1,] 648 736## [2,] 623 766## [3,] 1419 1036## [4,] 1630 1020## [5,] 1846 939## [6,] 1973 848## [7,] 2032 791## [8,] 2072 723## [9,] 2077 676## [10,] 2057 642## [11,] 2003 602## [12,] 1913 554## [13,] 1829 520## [14,] 1731 496## [15,] 1394 495## ## , , ori15## ## [,1] [,2]## [1,] 721 867## [2,] 721 893## [3,] 1549 1123## [4,] 1726 1107## [5,] 1826 1069## [6,] 1902 1036## [7,] 2018 955## [8,] 2055 895## [9,] 2062 860## [10,] 2050 810## [11,] 2011 768## [12,] 1933 710## [13,] 1832 655## [14,] 1648 625## [15,] 1545 622## ## , , ori16## ## [,1] [,2]## [1,] 943 743## [2,] 940 770## [3,] 1722 1007## [4,] 2027 925## [5,] 2104 878## [6,] 2169 830## [7,] 2230 775## [8,] 2252 735## [9,] 2275 700## [10,] 2271 660## [11,] 2213 606## [12,] 2144 573
## [13,] 2088 542## [14,] 2020 517## [15,] 1722 488
n <- dim(tudo1)[3] #número de indivíduos
#superimpose configurationssup <- gpagen(A = tudo1, ProcD = T, Proj = T)
## |
| | 0% |
|============= | 20% |
|========================== | 40% |
|=================================================================| 100%
names(sup)
## [1] "coords" "Csize" "iter" "points.VCV" ## [5] "points.var" "consensus" "p" "k" ## [9] "nsliders" "nsurf" "data" "Q" ## [13] "slide.method" "call"
tudo1 <- sup$coords #coordenadas sobrepostasdim(tudo1)
## [1] 15 2 16
tudo1
## , , ori1 ## ## [,1] [,2]## [1,] -0.41141968 0.003584539## [2,] -0.41016829 0.026467190## [3,] -0.21769177 0.250135576## [4,] -0.01564311 0.194983654## [5,] 0.03292593 0.167000003## [6,] 0.10739529 0.127992550## [7,] 0.16075954 0.092448512
## [8,] 0.20498298 0.058390595## [9,] 0.32084435 0.001126667## [10,] 0.21712019 -0.052791254## [11,] 0.16036732 -0.096743512## [12,] 0.10127709 -0.132588336## [13,] 0.03676838 -0.180990032## [14,] -0.04945354 -0.216951328## [15,] -0.23806468 -0.242064825## ## , , ori2 ## ## [,1] [,2]## [1,] -0.40143371 -0.006744274## [2,] -0.39944299 0.021374951## [3,] -0.20093338 0.255603082## [4,] -0.06214992 0.229817899## [5,] 0.03777037 0.187077651## [6,] 0.10854744 0.146540412## [7,] 0.17265335 0.105409955## [8,] 0.22824572 0.056596184## [9,] 0.30895168 -0.009433858## [10,] 0.19659395 -0.082100492## [11,] 0.15445189 -0.118131103## [12,] 0.11853256 -0.140342335## [13,] 0.01695268 -0.187333026## [14,] -0.05759739 -0.215750591## [15,] -0.22114224 -0.242584456## ## , , ori3 ## ## [,1] [,2]## [1,] -0.447696463 -0.001780098## [2,] -0.446277897 0.016802720## [3,] -0.242630227 0.246282687## [4,] 0.007855693 0.169094198## [5,] 0.064665979 0.130582339## [6,] 0.106280830 0.096244886## [7,] 0.159560457 0.063799026## [8,] 0.194742426 0.032806576## [9,] 0.296474042 -0.020176662## [10,] 0.198346161 -0.060483320## [11,] 0.161089001 -0.078681424## [12,] 0.121272498 -0.098658631## [13,] 0.077146179 -0.120266880## [14,] 0.040894938 -0.140301347## [15,] -0.291723617 -0.235264069## ## , , ori4 ## ## [,1] [,2]
## [1,] -0.42461617 -0.010518138## [2,] -0.42571742 0.020341522## [3,] -0.23865949 0.241182391## [4,] 0.01152129 0.184144309## [5,] 0.05163125 0.158737537## [6,] 0.09982253 0.127817385## [7,] 0.17638252 0.078717145## [8,] 0.22162288 0.044647729## [9,] 0.30822091 -0.007793855## [10,] 0.21971699 -0.038060211## [11,] 0.15688391 -0.090447431## [12,] 0.09359703 -0.124923778## [13,] 0.01340323 -0.171725978## [14,] -0.03415039 -0.192514912## [15,] -0.22965908 -0.219603717## ## , , ori5 ## ## [,1] [,2]## [1,] -0.400859326 -0.018340000## [2,] -0.401587293 0.004556281## [3,] -0.193439703 0.234257306## [4,] -0.047330713 0.212279019## [5,] 0.008639234 0.193899822## [6,] 0.109555656 0.147611654## [7,] 0.190737098 0.101613849## [8,] 0.250754692 0.051636990## [9,] 0.358484905 -0.003377464## [10,] 0.225426908 -0.067611400## [11,] 0.165184004 -0.102996029## [12,] 0.047987566 -0.162848353## [13,] -0.027741688 -0.185071958## [14,] -0.070063147 -0.196631514## [15,] -0.215748192 -0.208978204## ## , , ori6 ## ## [,1] [,2]## [1,] -0.43001605 0.007508726## [2,] -0.42659477 0.028719032## [3,] -0.17032161 0.244590694## [4,] -0.03247324 0.197172376## [5,] 0.02153886 0.166371843## [6,] 0.08622355 0.120758358## [7,] 0.14513014 0.082110501## [8,] 0.19936750 0.040157379## [9,] 0.29638866 -0.010774668## [10,] 0.22233134 -0.046823086## [11,] 0.18313511 -0.084274950## [12,] 0.12650831 -0.123779754
## [13,] 0.07343022 -0.166454845## [14,] -0.03730582 -0.209579465## [15,] -0.25734220 -0.245702143## ## , , ori7 ## ## [,1] [,2]## [1,] -0.42550079 -0.025281875## [2,] -0.42653854 0.005827410## [3,] -0.21518442 0.275583380## [4,] 0.04891699 0.180467923## [5,] 0.08474374 0.163799525## [6,] 0.12437974 0.140611975## [7,] 0.15137943 0.117130550## [8,] 0.19695188 0.081665913## [9,] 0.29473308 -0.001349024## [10,] 0.18084857 -0.070685284## [11,] 0.14134353 -0.109685531## [12,] 0.07870396 -0.149661380## [13,] 0.04992561 -0.164625277## [14,] -0.06170597 -0.204386808## [15,] -0.22299682 -0.239411499## ## , , ori8 ## ## [,1] [,2]## [1,] -0.40217058 -0.018230880## [2,] -0.40164584 0.009784791## [3,] -0.21719529 0.242151571## [4,] -0.03368417 0.216584190## [5,] 0.01669642 0.198498082## [6,] 0.11438269 0.158600099## [7,] 0.18185223 0.103250204## [8,] 0.23175723 0.055194860## [9,] 0.34554301 -0.030296354## [10,] 0.19969767 -0.079873197## [11,] 0.14375026 -0.113032110## [12,] 0.06656938 -0.151974917## [13,] 0.01632866 -0.183527968## [14,] -0.02919172 -0.195888015## [15,] -0.23268995 -0.211240356## ## , , ori9## ## [,1] [,2]## [1,] -0.54219385 0.0001219051## [2,] -0.54411166 0.0100810695## [3,] -0.16517670 0.1342128620## [4,] 0.03831884 0.1118293164## [5,] 0.11280618 0.0951210641
## [6,] 0.15223594 0.0764655430## [7,] 0.17333355 0.0609461246## [8,] 0.21496586 0.0410156570## [9,] 0.23330242 0.0207029637## [10,] 0.22559659 -0.0052883668## [11,] 0.18974033 -0.0371956147## [12,] 0.11469450 -0.0882356142## [13,] 0.02493600 -0.1324049077## [14,] -0.07892433 -0.1416903193## [15,] -0.14952367 -0.1456816827## ## , , ori10## ## [,1] [,2]## [1,] -0.52439805 -0.003567778## [2,] -0.54526133 0.006141455## [3,] -0.16697203 0.159855361## [4,] 0.01337269 0.138921849## [5,] 0.06723178 0.117650950## [6,] 0.11728582 0.090236238## [7,] 0.17405603 0.045665767## [8,] 0.22494438 0.011794143## [9,] 0.24435497 -0.012792621## [10,] 0.22345655 -0.029818900## [11,] 0.16926917 -0.055992343## [12,] 0.13480169 -0.082706524## [13,] 0.04619262 -0.121993659## [14,] -0.01065480 -0.131331612## [15,] -0.16767949 -0.132062326## ## , , ori11## ## [,1] [,2]## [1,] -0.56076011 0.001366836## [2,] -0.55564178 0.015124697## [3,] -0.20288043 0.151688628## [4,] 0.03332742 0.113880041## [5,] 0.09652735 0.084850370## [6,] 0.12818050 0.070604583## [7,] 0.18274750 0.026877883## [8,] 0.20455198 0.009807475## [9,] 0.21819360 -0.013941172## [10,] 0.19050466 -0.033766301## [11,] 0.16820167 -0.043806427## [12,] 0.13627675 -0.062921982## [13,] 0.10902870 -0.084836911## [14,] 0.06005235 -0.105941480## [15,] -0.20831017 -0.128986239## ## , , ori12
## ## [,1] [,2]## [1,] -0.56305122 -0.0217057856## [2,] -0.56360392 -0.0102612875## [3,] -0.16987770 0.1570619056## [4,] 0.08398738 0.1126682554## [5,] 0.12982204 0.0874466215## [6,] 0.16223313 0.0614531403## [7,] 0.18399459 0.0415411011## [8,] 0.20579271 0.0232854551## [9,] 0.21566079 0.0006547272## [10,] 0.19341524 -0.0098659570## [11,] 0.16910922 -0.0238908120## [12,] 0.11503848 -0.0555051402## [13,] 0.03881204 -0.0952479065## [14,] -0.03091807 -0.1257612071## [15,] -0.17041473 -0.1418731101## ## , , ori13## ## [,1] [,2]## [1,] -0.58443673 -0.0012178556## [2,] -0.57317082 0.0133383232## [3,] -0.15431669 0.1532975098## [4,] 0.05543398 0.1083234951## [5,] 0.10456713 0.0874340181## [6,] 0.14625152 0.0591346873## [7,] 0.16884067 0.0425453619## [8,] 0.19357927 0.0250379598## [9,] 0.21239415 0.0004893965## [10,] 0.19468126 -0.0212857484## [11,] 0.16334171 -0.0438029480## [12,] 0.12628777 -0.0658700415## [13,] 0.06758279 -0.0961119588## [14,] 0.02782657 -0.1115556496## [15,] -0.14886255 -0.1497565498## ## , , ori14## ## [,1] [,2]## [1,] -0.54915570 -0.007541623## [2,] -0.56264891 0.008110592## [3,] -0.14536324 0.163288099## [4,] -0.03172289 0.157176128## [5,] 0.08323578 0.117393726## [6,] 0.15176586 0.071069519## [7,] 0.18420428 0.041508441## [8,] 0.20667375 0.005985983## [9,] 0.21087451 -0.019214530## [10,] 0.19986681 -0.037860605
## [11,] 0.17153174 -0.060002343## [12,] 0.12425727 -0.086864912## [13,] 0.07982351 -0.106328634## [14,] 0.02783601 -0.120577441## [15,] -0.15117878 -0.126142400## ## , , ori15## ## [,1] [,2]## [1,] -0.57282301 -0.0001088834## [2,] -0.57285547 0.0151448043## [3,] -0.09400025 0.1507580940## [4,] 0.01115300 0.1408212574## [5,] 0.06949771 0.1186078831## [6,] 0.11406922 0.0991167738## [7,] 0.18134286 0.0521817307## [8,] 0.20330337 0.0172576828## [9,] 0.20855654 -0.0036441270## [10,] 0.20036846 -0.0329649475## [11,] 0.17725200 -0.0575902617## [12,] 0.13158308 -0.0914128154## [13,] 0.07266285 -0.1235309692## [14,] -0.03373068 -0.1411792175## [15,] -0.09637969 -0.1434570045## ## , , ori16## ## [,1] [,2]## [1,] -0.58403714 -0.002354455## [2,] -0.58624730 0.013537457## [3,] -0.13521942 0.167516115## [4,] 0.04557850 0.124874294## [5,] 0.09196605 0.098648376## [6,] 0.13140863 0.071499953## [7,] 0.16853772 0.040177975## [8,] 0.18280551 0.016832318## [9,] 0.19804367 -0.003902573## [10,] 0.19483163 -0.027795615## [11,] 0.16154769 -0.060457615## [12,] 0.12123332 -0.081374541## [13,] 0.08815699 -0.100921021## [14,] 0.04795683 -0.116956628## [15,] -0.12656267 -0.139324039
tipo <- c(rep("A", 8), rep("B", 8))tipo <- as.factor(tipo)tipo
## [1] A A A A A A A A B B B B B B B B## Levels: A B
#links between landmarkslink<-c(1 : 15, 1)
# Vamos representar as configurações superpostas com duas cores diferentes:plot(tudo1[,1,], tudo1[,2,], asp = 1, bg = 1, pch = 21, cex = 0.5)for (i in 1:n) {lines(tudo1[link,,i], col = (c(1, 2)[tipo])[i])}
Explorando a variação morfológica nos dados usando a função “prcomp”:# Antes, temos que rearranjar os dadosM <- matrix(NA, n, 15 * 2)for (i in 1:n){ M[i,] <- tudo1[,,i] }M #agora, temos os indivíduos nas linhas e os marcos nas colunas!
## [,1] [,2] [,3] [,4] [,5]## [1,] -0.4114197 -0.4101683 -0.21769177 -0.015643109 0.032925932## [2,] -0.4014337 -0.3994430 -0.20093338 -0.062149921 0.037770367## [3,] -0.4476965 -0.4462779 -0.24263023 0.007855693 0.064665979## [4,] -0.4246162 -0.4257174 -0.23865949 0.011521293 0.051631245## [5,] -0.4008593 -0.4015873 -0.19343970 -0.047330713 0.008639234## [6,] -0.4300160 -0.4265948 -0.17032161 -0.032473236 0.021538855
## [7,] -0.4255008 -0.4265385 -0.21518442 0.048916993 0.084743736## [8,] -0.4021706 -0.4016458 -0.21719529 -0.033684173 0.016696418## [9,] -0.5421939 -0.5441117 -0.16517670 0.038318837 0.112806178## [10,] -0.5243981 -0.5452613 -0.16697203 0.013372688 0.067231780## [11,] -0.5607601 -0.5556418 -0.20288043 0.033327417 0.096527347## [12,] -0.5630512 -0.5636039 -0.16987770 0.083987382 0.129822043## [13,] -0.5844367 -0.5731708 -0.15431669 0.055433976 0.104567127## [14,] -0.5491557 -0.5626489 -0.14536324 -0.031722888 0.083235778## [15,] -0.5728230 -0.5728555 -0.09400025 0.011153004 0.069497709## [16,] -0.5840371 -0.5862473 -0.13521942 0.045578500 0.091966054## [,6] [,7] [,8] [,9] [,10] [,11]## [1,] 0.10739529 0.1607595 0.2049830 0.3208443 0.2171202 0.1603673## [2,] 0.10854744 0.1726533 0.2282457 0.3089517 0.1965940 0.1544519## [3,] 0.10628083 0.1595605 0.1947424 0.2964740 0.1983462 0.1610890## [4,] 0.09982253 0.1763825 0.2216229 0.3082209 0.2197170 0.1568839## [5,] 0.10955566 0.1907371 0.2507547 0.3584849 0.2254269 0.1651840## [6,] 0.08622355 0.1451301 0.1993675 0.2963887 0.2223313 0.1831351## [7,] 0.12437974 0.1513794 0.1969519 0.2947331 0.1808486 0.1413435## [8,] 0.11438269 0.1818522 0.2317572 0.3455430 0.1996977 0.1437503## [9,] 0.15223594 0.1733336 0.2149659 0.2333024 0.2255966 0.1897403## [10,] 0.11728582 0.1740560 0.2249444 0.2443550 0.2234565 0.1692692## [11,] 0.12818050 0.1827475 0.2045520 0.2181936 0.1905047 0.1682017## [12,] 0.16223313 0.1839946 0.2057927 0.2156608 0.1934152 0.1691092## [13,] 0.14625152 0.1688407 0.1935793 0.2123941 0.1946813 0.1633417## [14,] 0.15176586 0.1842043 0.2066738 0.2108745 0.1998668 0.1715317## [15,] 0.11406922 0.1813429 0.2033034 0.2085565 0.2003685 0.1772520## [16,] 0.13140863 0.1685377 0.1828055 0.1980437 0.1948316 0.1615477## [,12] [,13] [,14] [,15] [,16]## [1,] 0.10127709 0.03676838 -0.04945354 -0.23806468 0.0035845392## [2,] 0.11853256 0.01695268 -0.05759739 -0.22114224 -0.0067442736## [3,] 0.12127250 0.07714618 0.04089494 -0.29172362 -0.0017800975## [4,] 0.09359703 0.01340323 -0.03415039 -0.22965908 -0.0105181378## [5,] 0.04798757 -0.02774169 -0.07006315 -0.21574819 -0.0183399999## [6,] 0.12650831 0.07343022 -0.03730582 -0.25734220 0.0075087263## [7,] 0.07870396 0.04992561 -0.06170597 -0.22299682 -0.0252818747## [8,] 0.06656938 0.01632866 -0.02919172 -0.23268995 -0.0182308804## [9,] 0.11469450 0.02493600 -0.07892433 -0.14952367 0.0001219051## [10,] 0.13480169 0.04619262 -0.01065480 -0.16767949 -0.0035677782## [11,] 0.13627675 0.10902870 0.06005235 -0.20831017 0.0013668356## [12,] 0.11503848 0.03881204 -0.03091807 -0.17041473 -0.0217057856## [13,] 0.12628777 0.06758279 0.02782657 -0.14886255 -0.0012178556## [14,] 0.12425727 0.07982351 0.02783601 -0.15117878 -0.0075416234## [15,] 0.13158308 0.07266285 -0.03373068 -0.09637969 -0.0001088834## [16,] 0.12123332 0.08815699 0.04795683 -0.12656267 -0.0023544548## [,17] [,18] [,19] [,20] [,21] [,22]## [1,] 0.026467190 0.2501356 0.1949837 0.16700000 0.12799255 0.09244851## [2,] 0.021374951 0.2556031 0.2298179 0.18707765 0.14654041 0.10540996
## [3,] 0.016802720 0.2462827 0.1690942 0.13058234 0.09624489 0.06379903## [4,] 0.020341522 0.2411824 0.1841443 0.15873754 0.12781739 0.07871715## [5,] 0.004556281 0.2342573 0.2122790 0.19389982 0.14761165 0.10161385## [6,] 0.028719032 0.2445907 0.1971724 0.16637184 0.12075836 0.08211050## [7,] 0.005827410 0.2755834 0.1804679 0.16379953 0.14061198 0.11713055## [8,] 0.009784791 0.2421516 0.2165842 0.19849808 0.15860010 0.10325020## [9,] 0.010081070 0.1342129 0.1118293 0.09512106 0.07646554 0.06094612## [10,] 0.006141455 0.1598554 0.1389218 0.11765095 0.09023624 0.04566577## [11,] 0.015124697 0.1516886 0.1138800 0.08485037 0.07060458 0.02687788## [12,] -0.010261288 0.1570619 0.1126683 0.08744662 0.06145314 0.04154110## [13,] 0.013338323 0.1532975 0.1083235 0.08743402 0.05913469 0.04254536## [14,] 0.008110592 0.1632881 0.1571761 0.11739373 0.07106952 0.04150844## [15,] 0.015144804 0.1507581 0.1408213 0.11860788 0.09911677 0.05218173## [16,] 0.013537457 0.1675161 0.1248743 0.09864838 0.07149995 0.04017797## [,23] [,24] [,25] [,26] [,27]## [1,] 0.058390595 0.0011266666 -0.052791254 -0.09674351 -0.13258834## [2,] 0.056596184 -0.0094338582 -0.082100492 -0.11813110 -0.14034234## [3,] 0.032806576 -0.0201766620 -0.060483320 -0.07868142 -0.09865863## [4,] 0.044647729 -0.0077938546 -0.038060211 -0.09044743 -0.12492378## [5,] 0.051636990 -0.0033774644 -0.067611400 -0.10299603 -0.16284835## [6,] 0.040157379 -0.0107746682 -0.046823086 -0.08427495 -0.12377975## [7,] 0.081665913 -0.0013490239 -0.070685284 -0.10968553 -0.14966138## [8,] 0.055194860 -0.0302963540 -0.079873197 -0.11303211 -0.15197492## [9,] 0.041015657 0.0207029637 -0.005288367 -0.03719561 -0.08823561## [10,] 0.011794143 -0.0127926207 -0.029818900 -0.05599234 -0.08270652
## [11,] 0.009807475 -0.0139411718 -0.033766301 -0.04380643 -0.06292198## [12,] 0.023285455 0.0006547272 -0.009865957 -0.02389081 -0.05550514## [13,] 0.025037960 0.0004893965 -0.021285748 -0.04380295 -0.06587004## [14,] 0.005985983 -0.0192145298 -0.037860605 -0.06000234 -0.08686491## [15,] 0.017257683 -0.0036441270 -0.032964947 -0.05759026 -0.09141282## [16,] 0.016832318 -0.0039025727 -0.027795615 -0.06045762 -0.08137454## [,28] [,29] [,30]## [1,] -0.18099003 -0.2169513 -0.2420648## [2,] -0.18733303 -0.2157506 -0.2425845## [3,] -0.12026688 -0.1403013 -0.2352641## [4,] -0.17172598 -0.1925149 -0.2196037## [5,] -0.18507196 -0.1966315 -0.2089782## [6,] -0.16645484 -0.2095795 -0.2457021## [7,] -0.16462528 -0.2043868 -0.2394115## [8,] -0.18352797 -0.1958880 -0.2112404## [9,] -0.13240491 -0.1416903 -0.1456817## [10,] -0.12199366 -0.1313316 -0.1320623## [11,] -0.08483691 -0.1059415 -0.1289862## [12,] -0.09524791 -0.1257612 -0.1418731## [13,] -0.09611196 -0.1115556 -0.1497565## [14,] -0.10632863 -0.1205774 -0.1261424## [15,] -0.12353097 -0.1411792 -0.1434570## [16,] -0.10092102 -0.1169566 -0.1393240
pca <- prcomp(M)names(pca)
## [1] "sdev" "rotation" "center" "scale" "x"
# calculando-se a porcentagem de variância explicada pelos eixos:barplot(pca$sdev^2 / sum(pca$sdev^2))
# Vamos plotar os espécimes, com símbolos diferentes para# os dois grupos de folhasplot(pca$x[,1:2], pch=c(21,22)[tipo], xlab = "PC1", ylab = "PC2")
Podemos usar esses valores ainda para algumas inferências estatísticas:# variância dos autovalores:pca$sdev #autovalores
## [1] 1.861223e-01 6.052338e-02 4.746342e-02 3.637415e-02 3.119541e-02## [6] 1.893293e-02 1.443687e-02 1.313641e-02 1.248057e-02 9.873369e-03## [11] 8.324841e-03 6.894398e-03 4.497319e-03 3.973928e-03 1.956900e-03## [16] 2.739914e-17
t1 <- var(pca$sdev) #variância dos autovalorest1
## [1] 0.002066424
t2 <- sum(pca$sdev) #variância totalt2
## [1] 0.4561862
TT <- t1 / t2 ^ 2 #variância escalonada dos autovaloresTT
## [1] 0.009929679
mi <- (16 - 1) / (16 ^ 2) #máximo do índice escalonadoveig <- TT / miveig #variância na forma
## [1] 0.1694665
