MATLAB与R语言结合：Hiebeler参考手册

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"Hiebeler-matlabR" 这篇文档是David Hiebeler在2010年5月25日编写的MATLAB和R语言的参考指南，旨在帮助他在教学过程中，尤其是在教授建模与仿真课程时，将R语言引入到MATLAB为主的课堂中。这门课程涉及人口和流行病学建模，涵盖了确定性和随机模型，以及离散和连续时间的模型，还有空间模型。在教学安排上，一半时间在常规教室进行理论讲解，另一半时间在计算机实验室让学生实践建模与仿真。在之前的课程版本中，Hiebeler只使用MATLAB。但在2007年的春季学期，一些生物专业的研究生，他们之前学习过R语言，请求在课堂上也使用R，Hiebeler同意了。在他的同事Bill Halteman的帮助下，他迅速学习R语言，并将新学到的内容及时添加到这个参考指南中，以便于日后查阅和教学。文档中记录了Hiebeler在学习R语言过程中遇到的各种问题和解决方法，他花费大量时间寻找简单易行的解决方案。这个参考指南因此包含了从MATLAB转换到R的一些关键操作和技巧，对于那些同时使用或打算从MATLAB过渡到R的用户来说，是非常有价值的学习资源。虽然没有提供具体的内容，但我们可以推断，这个文档可能涵盖以下方面： 1. MATLAB与R的语法对比：包括数据类型、变量声明、数组操作、函数定义等方面的比较。 2. 数据处理：如何在R中进行数据导入、清洗、转换和分析，以及与MATLAB中的类似操作。 3. 数学和统计函数：MATLAB常用的数学和统计功能在R中的等价实现。 4. 画图和可视化：MATLAB的图形功能与R的ggplot2或lattice库的使用。 5. 仿真和模型构建：如何在R中建立和运行仿真模型，特别是在流行病学和人口模型方面的应用。 6. 控制流和编程结构：理解R中的循环、条件语句和函数调用，与MATLAB的不同之处。 7. 编程效率提升：R中的向量化操作和使用apply家族函数提高代码效率。 8. 软件集成：如何在MATLAB环境中调用R（如使用RInside库），或者反之。这个参考指南对于那些希望将MATLAB的知识应用到R环境的用户来说，是一份宝贵的参考资料，可以帮助他们快速理解和适应R语言，同时保持在MATLAB中的工作习惯。

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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