Arithmetic with matrices

TODO

• link to linearAlgebra

Sums and means

age    <- c(19, 19, 31, 19, 24)
weight <- c(95, 76, 94, 76, 76)
height <- c(197, 178, 189, 184, 173)
(mat   <- cbind(age, weight, height))

     age weight height
[1,]  19     95    197
[2,]  19     76    178
[3,]  31     94    189
[4,]  19     76    184
[5,]  24     76    173

sum(mat)

[1] 1450

rowSums(mat)

[1] 311 273 314 279 273

mean(mat)

[1] 96.66667

colMeans(mat)

   age weight height 
  22.4   83.4  184.2 

Apply any arithmetic function to rows or columns

apply(mat, 2, sum)

   age weight height 
   112    417    921 

apply(mat, 1, max)

[1] 197 178 189 184 173

apply(mat, 1, range)

     [,1] [,2] [,3] [,4] [,5]
[1,]   19   19   31   19   24
[2,]  197  178  189  184  173

apply(mat, 2, mean, trim=0.1)

   age weight height 
  22.4   83.4  184.2 

Matrix algebra

Mj <- rowMeans(mat)
Mk <- colMeans(mat)
sweep(mat, 1, Mj, "-")

           age     weight   height
[1,] -84.66667  -8.666667 93.33333
[2,] -72.00000 -15.000000 87.00000
[3,] -73.66667 -10.666667 84.33333
[4,] -74.00000 -17.000000 91.00000
[5,] -67.00000 -15.000000 82.00000

t(scale(t(mat), center=TRUE, scale=FALSE))

           age     weight   height
[1,] -84.66667  -8.666667 93.33333
[2,] -72.00000 -15.000000 87.00000
[3,] -73.66667 -10.666667 84.33333
[4,] -74.00000 -17.000000 91.00000
[5,] -67.00000 -15.000000 82.00000
attr(,"scaled:center")
[1] 103.6667  91.0000 104.6667  93.0000  91.0000

sweep(mat, 2, Mk, "-")

      age weight height
[1,] -3.4   11.6   12.8
[2,] -3.4   -7.4   -6.2
[3,]  8.6   10.6    4.8
[4,] -3.4   -7.4   -0.2
[5,]  1.6   -7.4  -11.2

scale(mat, center=TRUE, scale=FALSE)

      age weight height
[1,] -3.4   11.6   12.8
[2,] -3.4   -7.4   -6.2
[3,]  8.6   10.6    4.8
[4,] -3.4   -7.4   -0.2
[5,]  1.6   -7.4  -11.2
attr(,"scaled:center")
   age weight height 
  22.4   83.4  184.2 

Covariance and correlation matrices

cov(mat)

         age weight height
age    27.80  22.55    0.4
weight 22.55 102.80   82.4
height  0.40  82.40   87.7

cor(mat)

               age    weight      height
age    1.000000000 0.4218204 0.008100984
weight 0.421820411 1.0000000 0.867822404
height 0.008100984 0.8678224 1.000000000

cov.wt(mat, method="ML")

$cov
         age weight height
age    22.24  18.04   0.32
weight 18.04  82.24  65.92
height  0.32  65.92  70.16

$center
   age weight height 
  22.4   83.4  184.2 

$n.obs
[1] 5

diag(cov(mat))

   age weight height 
  27.8  102.8   87.7 

vec <- rnorm(nrow(mat))
cor(mat, vec)

              [,1]
age     0.17497156
weight  0.14332530
height -0.04030174

cor(vec, mat)

           age    weight      height
[1,] 0.1749716 0.1433253 -0.04030174

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