MATLAB用户指南：从R语言入门

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"R for Matlab用户指南" 这篇文档是由David Hiebeler撰写的，旨在帮助熟悉Matlab的用户过渡到使用R语言。Hiebeler在2007年春季学期教授建模与仿真课程时，为了适应学生对R语言的需求，开始编写这份参考手册。课程涉及人口和流行病学模型，包括确定性和随机模型，以及连续和离散时间的模型，还有空间模型。起初，课程基于Matlab，但一些生物研究生由于在统计课程中学习过R，希望在Hiebeler的课上也能使用R，他便同意了，并在同事Bill Halteman的帮助下快速学习R。文档的核心是记录了Hiebeler在教学过程中学到的R语言操作，以便日后查阅和教学。每次他在R中实现课程中的某个功能，都会将其添加到参考指南中，这其中包括了大量搜索简洁方法的时间。因此，这份指南对于从Matlab转用R的用户来说，是一个宝贵的资源，它涵盖了如何在R中执行类似于Matlab的任务，比如数值计算、数据处理、建模和可视化等。在R语言中，用户可以找到类似Matlab的矩阵运算功能，如向量和矩阵的创建、操作和计算。R提供了丰富的统计分析包，这对于进行数据探索和建模特别有用，而这是Matlab可能需要额外模块才能完成的。此外，R有强大的绘图能力，能够制作出高质量的统计图形，这在Matlab中也需要额外的编程工作。转换到R的一个显著优势是其开源性质，这意味着有大量的社区支持和不断更新的包，这些包可以扩展R的功能，使其能够处理各种各样的任务，从机器学习到地理信息系统（GIS）。R的语法虽然与Matlab有所不同，但一旦熟悉，就能发现R的灵活性和效率。 “R for Matlab users”是一个宝贵的教学资源，它帮助用户理解和应用R语言来解决在Matlab中习惯处理的问题。通过这个指南，用户可以逐步了解R的基本结构和命令，从而在数据分析和建模领域实现平滑过渡。

D. Hiebeler, Matlab / R Reference 9

No. Description Matlab R

98 Singular-value decomposi-

tion: given m × n matrix

A with rank r, ﬁnd m × r

matrix P with orthonormal

columns, diagonal r × r

matrix S, and r × n matrix

with orthonormal rows

so that P SQ

= A

[P,S,Q]=svd(A,’econ’) tmp=svd(A); U=tmp$u; V=tmp$v;

S=diag(tmp$d)

99 Schur decomposi-

tion of square matrix,

A = QT Q

= QT Q

−1

where

Q is unitary (i.e. Q

Q = I)

and T is upper triangular;

is the Hermitian

(conjugate) transpose

[Q,T]=schur(A) tmp=Schur(Matrix(A)); T=tmp@T;

Q=tmp@Q Note that Schur is part of

the Matrix package (see item 331 for

how to install/load packages). T and

Q will be of class Matrix rather than

class matrix; to make them the latter,

instead do T=as.matrix(tmp@T) and

Q=as.matrix(tmp@Q) above.

100 Cholesky factorization of a

square, symmetric, positive

deﬁnite matrix A = R

where R is upper-triangular

R = chol(A) R = chol(A) Note that chol is part

of the Matrix package (see item 331

for how to install/load packages).

101 QR factorization of matrix A,

where Q is orthogonal (sat-

isfying QQ

= I) and R is

upper-triangular

[Q,R]=qr(A) satisfying QR = A, or

[Q,R,E]=qr(A) to do permuted QR

factorization satisfying AE = QR

z=qr(A); Q=qr.Q(z); R=qr.R(z);

E=diag(n)[,z$pivot] (where n is

the number of columns in A) gives

permuted QR factorization satisfying

AE = QR

102 Vector norms norm(v,1) for 1-norm k~vk

norm(v,2) for Euclidean norm

k~vk

, norm(v,inf) for inﬁnity-norm

k~vk

∞

, and norm(v,p) for p-norm

k~vk

= (

)

1/p

R does not have a norm func-

tion for vectors; only one for

matrices. But the following will

work: norm(matrix(v),’1’) for

1-norm k~vk

, norm(matrix(v),’i’)

for inﬁnity-norm k~vk

∞

, and

sum(abs(v)^p)^(1/p) for p-norm

k~vk

= (

)

1/p

103 Matrix norms norm(A,1) for 1-norm kAk

norm(A) for 2-norm kAk

norm(A,inf) for inﬁnity-norm

kAk

∞

, and norm(A,’fro’) for

Frobenius norm

1/2

norm(A,’1’) for 1-norm kAk

max(svd(A)$d) for 2-norm kAk

norm(A,’i’) for inﬁnity-norm kAk

∞

and norm(A,’f’) for Frobenius norm

1/2

104 Condition number cond(A) =

kAk

−1

of A, using 1-

norm

cond(A,1) (Note: Matlab also has

a function rcond(A) which computes

reciprocal condition estimator using

the 1-norm)

1/rcond(A,’1’)

105 Condition number cond(A) =

kAk

−1

of A, using 2-

norm

cond(A,2) kappa(A, exact=TRUE) (leave out

the “exact=TRUE” for an esti-

mate)

106 Condition number cond(A) =

kAk

∞

−1

∞

of A, using

inﬁnity-norm

cond(A,inf) 1/rcond(A,’I’)

D. Hiebeler, Matlab / R Reference 10

No. Description Matlab R

107 Compute mean of all ele-

ments in vector or matrix

mean(v) for vectors, mean(A(:)) for

matrices

mean(v) or mean(A)

108 Compute means of columns

of a matrix

mean(A) colMeans(A)

109 Compute means of rows of a

matrix

mean(A,2) rowMeans(A)

110 Compute standard deviation

of all elements in vector or

matrix

std(v) for vectors, std(A(:)) for

matrices. This normalizes by n − 1.

Use std(v,1) to normalize by n.

sd(v) for vectors, sd(c(A)) for ma-

trices. This normalizes by n − 1.

111 Compute standard deviations

of columns of a matrix

std(A). This normalizes by n − 1.

Use std(A,1) to normalize by n

sd(A). This normalizes by n − 1.

112 Compute standard deviations

of rows of a matrix

std(A,0,2) to normalize by n − 1,

std(A,1,2) to normalize by n

apply(A,1,sd). This normalizes by

n − 1.

113 Compute variance of all ele-

ments in vector or matrix

var(v) for vectors, var(A(:)) for

matrices. This normalizes by n − 1.

Use var(v,1) to normalize by n.

var(v) for vectors, var(c(A)) for

matrices. This normalizes by n − 1.

114 Compute variance of columns

of a matrix

var(A). This normalizes by n − 1.

Use var(A,1) to normalize by n

apply(A,2,var). This normalizes by

n − 1.

115 Compute variance of rows of

a matrix

var(A,0,2) to normalize by n − 1,

var(A,1,2) to normalize by n

apply(A,1,var). This normalizes by

n − 1.

116 Compute covariance for two

vectors of observations

cov(v,w) computes the 2 × 2 co-

variance matrix; the oﬀ-diagonal ele-

ments give the desired covariance

cov(v,w)

117 Compute covariance matrix,

giving covariances between

columns of matrix A

cov(A) var(A) or cov(A)

118 Given matrices A and B,

build covariance matrix C

where c

is the covariance be-

tween column i of A and col-

umn j of B

I don’t know of a direct way to

do this in Matlab. But one way is

[Y,X]=meshgrid(std(B),std(A));

X.*Y.*corr(A,B)

cov(A,B)

119 Compute Pearson’s linear

correlation coeﬃcient be-

tween elements of vectors v

and w

corr(v,w) Note: v and w must

be column vectors. To make it

work regardless of whether they

are row or column vectors, do

corr(v(:),w(:))

cor(v,w)

120 Compute Kendall’s tau corre-

lation statistic for vectors v

and w

corr(v,w,’type’,’kendall’) cor(v,w,method=’kendall’)

121 Compute Spearman’s rho

correlation statistic for

vectors v and w

corr(v,w,’type’,’spearman’) cor(v,w,method=’spearman’)

122 Compute pairwise Pearson’s

correlation coeﬃcient be-

tween columns of matrix

corr(A) The ’type’ argument may

also be used as in the previous two

items

cor(A) The method argument may

also be used as in the previous two

items

123 Compute matrix C of pair-

wise Pearson’s correlation co-

eﬃcients between each pair of

columns of matrices A and B,

i.e. so c

is the correlation

between column i of A and

column j of B

corr(A,B) The ’type’ argument

may also be used as just above

cor(A,B) The method argument

may also be used as just above

D. Hiebeler, Matlab / R Reference 11

No. Description Matlab R

124 Compute sum of all elements

in vector or matrix

sum(v) for vectors, sum(A(:)) for

matrices

sum(v) or sum(A)

125 Compute sums of columns of

matrix

sum(A) colSums(A)

126 Compute sums of rows of ma-

trix

sum(A,2) rowSums(A)

127 Compute product of all ele-

ments in vector or matrix

prod(v) for vectors, prod(A(:)) for

matrices

prod(v) or prod(A)

128 Compute products of

columns of matrix

prod(A) apply(A,2,prod)

129 Compute products of rows of

matrix

prod(A,2) apply(A,1,prod)

130 Compute matrix exponential

∞

k=0

/k!

expm(A) expm(Matrix(A)), but this is part of

the Matrix package which you’ll need

to install (see item 331 for how to in-

stall/load packages).

131 Compute cumulative sum of

values in vector

cumsum(v) cumsum(v)

132 Compute cumulative sums of

columns of matrix

cumsum(A) apply(A,2,cumsum)

133 Compute cumulative sums of

rows of matrix

cumsum(A,2) t(apply(A,1,cumsum))

134 Compute cumulative sum

of all elements of matrix

(column-by-column)

cumsum(A(:)) cumsum(A)

135 Cumulative product of ele-

ments in vector v

cumprod(v) (Can also be used in the

various ways cumsum can)

cumprod(v) (Can also be used in the

various ways cumsum can)

136 Cumulative minimum or

maximum of elements in

vector v

I don’t know of an easy way to do

this in Matlab

cummin(v) or cummax(v)

137 Compute diﬀerences between

consecutive elements of vec-

tor v. Result is a vector

w 1 element shorter than v,

where element i of w is ele-

ment i+1 of v minus element

i of v

diff(v) diff(v)

138 Make a vector y the same size

as vector x, which equals 4

everywhere that x is greater

than 5, and equals 3 every-

where else (done via a vector-

ized computation).

z = [3 4]; y = z((x > 5)+1) y = ifelse(x > 5, 4, 3)

139 Compute minimum of values

in vector v

min(v) min(v)

140 Compute minimum of all val-

ues in matrix A

min(A(:)) min(A)

141 Compute minimum value of

each column of matrix A

min(A) (returns a row vector) apply(A,2,min) (returns a vector)

142 Compute minimum value of

each row of matrix A

min(A, [ ], 2) (returns a column

vector)

apply(A,1,min) (returns a vector)

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