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首页快速上手的R编程教材——牛津大学讲座总结

快速上手的R编程教材——牛津大学讲座总结

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The R Programming lecture notes from the University of Oxford provide a concise and quick introduction to R programming. The course, taught by Robin Evans and conducted in Michaelmas 2014, covers the essentials of R programming in a fast-paced and efficient manner. The lectures take place at 10am on Mondays and Wednesdays, with practicals at 9am on Tuesdays and Thursdays. There is a significant overlap between the lecture and practical formats, enabling students to reinforce their learning through hands-on practice. Students are encouraged to bring their own laptops to class and ensure that R is installed and working properly. The course webpage, hosted at http://www.stats.ox.ac.uk/~evans/teaching.htm, provides additional resources and information for students. In the event that students do not have access to a laptop, arrangements can be made to accommodate their needs. Overall, the R Programming lecture notes from the University of Oxford offer a comprehensive yet succinct guide to mastering R programming. By following along with the course materials and engaging in practical exercises, students can quickly become proficient in using R for data analysis and statistical modeling.

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[1,] 1 1 1 1

[2,] 2 2 2 2

[3,] 3 3 3 3

Sometimes it’s useful to specify the elements by row ﬁrst

> matrix(1:12, nrow=3, byrow=TRUE)

There are special functions for constructing certain matrices:

> diag(3)

[,1] [,2] [,3]

[1,] 1 0 0

[2,] 0 1 0

[3,] 0 0 1

> diag(1:3)

[,1] [,2] [,3]

[1,] 1 0 0

[2,] 0 2 0

[3,] 0 0 3

> 1:5 %o% 1:5

[,1] [,2] [,3] [,4] [,5]

[1,] 1 2 3 4 5

[2,] 2 4 6 8 10

[3,] 3 6 9 12 15

[4,] 4 8 12 16 20

[5,] 5 10 15 20 25

The last operator performs an outer product, so it creates a matrix with

(i, j)-th entry x

. The function outer() generalizes this to any function

f on two arguments, to create a matrix with entries f(x

, y

). (More on

functions later.)

> outer(1:3, 1:4, "+")

[,1] [,2] [,3] [,4]

[1,] 2 3 4 5

[2,] 3 4 5 6

[3,] 4 5 6 7

Matrix multiplication is performed using the operator %*%, which is quite

distinct from scalar multiplication *.

> A <- matrix(c(1:8,10), 3, 3)

> x <- c(1,2,3)

> A %*% x # matrix multiplication

[,1]

[1,] 30

[2,] 36

[3,] 45

> A*x # NOT matrix multiplication

[,1] [,2] [,3]

[1,] 1 4 7

[2,] 4 10 16

[3,] 9 18 30

Standard functions exist for common mathematical operations on matrices.

> t(A) # transpose

[,1] [,2] [,3]

[1,] 1 2 3

[2,] 4 5 6

[3,] 7 8 10

> det(A) # determinant

[1] -3

> diag(A) # diagonal

[1] 1 5 10

> solve(A) # inverse

[,1] [,2] [,3]

[1,] -0.6667 -0.6667 1

[2,] -1.3333 3.6667 -2

[3,] 1.0000 -2.0000 1

Exercise 2.7. Construct the matrix

B =





1 2 3

4 2 6

−3 −1 −3





Show that B × B × B is a scalar multiple of the identity matrix, and ﬁnd

the scalar.

Matrices can be subsetted much the same way as vectors, although of course

they have two indices. Row number comes ﬁrst:

> A[2,1]

[1] 2

> A[2,2:ncol(A)]

[1] 5 8

> A[,1:2] # blank indices give everything

[,1] [,2]

[1,] 1 4

[2,] 2 5

[3,] 3 6

> A[c(),1:2] # empty indices give nothing!

[,1] [,2]

Notice that, where appropriate, R automatically reduces a matrix to a vector

or scalar when you subset it. You can override this using the optional drop

argument.

> A[2,2:ncol(A),drop=FALSE] # returns a matrix

[,1] [,2]

[1,] 5 8

You can stitch matrices together using the rbind() and cbind() functions.

These employ vector recycling:

> cbind(A, t(A))

[,1] [,2] [,3] [,4] [,5] [,6]

[1,] 1 4 7 1 2 3

[2,] 2 5 8 4 5 6

[3,] 3 6 10 7 8 10

> rbind(A, 1, 0)

[,1] [,2] [,3]

[1,] 1 4 7

[2,] 2 5 8

[3,] 3 6 10

[4,] 1 1 1

[5,] 0 0 0

Exercise 2.8. Construct the following matrices:

(a)



1 3 5 7

2 4 6 8



(b)







1 −1 1 · · · −1







(dimensions 15 × 10).







1 1 1 0 0 · · · 0 0

0 0 0 1 1 · · · 0 0

0 0 0 0 0 · · · 1 1







(dimensions 5 × 15).

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