# MatlabR.dvi Hiebeler Matlab R

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1 MATLAB °R / R Reference May 25, 2010 David Hiebeler Dept. of Mathematics and Statistics University of Maine Orono, ME 04469-5752 http://www.math.umaine.edu/~hiebeler I wrote the first version of this reference during the Spring 2007 semester, as I learned R while teaching my Modeling & Simulation course at the University of Maine. The course covers population and epidemiological modeling, including deterministic and stochastic models in discrete and continuous time, along with spatial models. Half of the class meetings are in a regular classroom, and half are in a computer lab where students work through modeling & simulation exercises. When I taught earlier versions of the course, it was based on Matlab only. In Spring 2007, some biology graduate students in the class who had learned R in statistics courses asked if they could use R in my class as well, and I said yes. My colleague Bill Halteman was a great help as I frantically learned R to stay ahead of the class. As I went, every time I learned how to do something in R for the course, I added it to this reference, so that I wouldn’t forget it later. Some items took a huge amount of time searching for a simple way to do what I wanted, but at the end of the semester, I was pleasantly surprised that almost everything I do in Matlab had an equivalent in R. I was also inspired to do this after seeing the “R for Octave Users” reference written by Robin Hankin. I’ve continued to add to the document, with many additions based on topics that came up while teaching courses on Advanced Linear Algebra and Numerical Analysis. This reference is organized into general categories. There is also a Matlab index and an R index at the end, which should make it easy to look up a command you know in one of the languages and learn how to do it in the other (or if you’re trying to read code in whichever language is unfamiliar to you, allow you to translate back to the one you are more familiar with). The index entries refer to the item numbers in the first column of the reference document, rather than page numbers. Any corrections, suggested improvements, or even just notification that the reference has been useful are appreciated. I hope all the time I spent on this will prove useful for others in addition to myself and my students. Note that sometimes I don’t necessarily do things in what you may consider the “best” way in a particular language. I often tried to do things in a similar way in both languages, and where possible I’ve avoided the use of Matlab toolboxes or R packages which are not part of the core distributions. But if you believe you have a “better” way (either simpler, or more computationally efficient) to do something, feel free to let me know. Acknowledgements: Thanks to Alan Cobo-Lewis and Isaac Michaud for correcting some errors; and Robert Bryce, Thomas Clerc, Richard Cotton, Stephen Eglen, Andreas Handel, Niels Richard Hansen, David Khabie-Zeitoune, Michael Kiparsky, Andy Moody, Ben Morin, Lee Pang, Manas A. Pathak, Rachel Rier, Rune Schjellerup Philosof, and Corey Yanofsky for contributions. Permission is granted to make and distribute verbatim copies of this manual provided this permission notice is preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions, except that this permission notice may be stated in a translation approved by the Free Software Foundation. c Copyright °2007–2010 David Hiebeler D. Hiebeler, Matlab / R Reference 2 Contents 1 Help 3 2 Entering/building/indexing matrices 2.1 Cell arrays and lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Structs and data frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 6 6 3 Computations 3.1 Basic computations . . . . . . . . . . 3.2 Complex numbers . . . . . . . . . . 3.3 Matrix/vector computations . . . . . 3.4 Root-finding . . . . . . . . . . . . . . 3.5 Function optimization/minimization 3.6 Numerical integration / quadrature . 3.7 Curve fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 6 7 8 14 14 15 16 4 Conditionals, control structure, loops 17 5 Functions, ODEs 21 6 Probability and random values 23 7 Graphics 7.1 Various types of plotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Printing/saving graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Animating cellular automata / lattice simulations . . . . . . . . . . . . . . . . . . . . . . . 27 27 35 36 8 Working with files 37 9 Miscellaneous 9.1 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Strings and Misc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 38 39 10 Spatial Modeling 42 Index of MATLAB commands and concepts 43 Index of R commands and concepts 48 D. Hiebeler, Matlab / R Reference 1 No. 1 3 Help Description Show help for a function (e.g. sqrt) Show help for a built-in keyword (e.g. for) General list of many help topics Matlab help sqrt, or helpwin sqrt to see it in a separate window help for R help(sqrt) or ?sqrt help 4 Explore main documentation in browser 5 Search documentation for keyword or partial keyword (e.g. functions which refer to “binomial”) doc or helpbrowser (previously it was helpdesk, which is now being phased out) lookfor binomial library() to see available libraries, or library(help=’base’) for very long list of stuff in base package which you can see help for help.start() 2 3 2 No. 6 7 Description Enter a row ¤ vector ~v £ 1 2 3 4 = 1 2 Enter a column vector 3 4 · 1 2 4 5 3 6 ¸ Enter a matrix 9 10 Access an element of vector v Access an element of matrix A Access an element of matrix A using a single index: indices count down the first column, then down the second column, etc. Build the vector [2 3 4 5 6 7] Build the vector [7 6 5 4 3 2] Build the vector [2 5 8 11 14] 12 13 14 help.search(’binomial’) Entering/building/indexing matrices 8 11 help(’for’) or ?’for’ Matlab v=[1 2 3 4] R v=c(1,2,3,4) or alternatively v=scan() then enter “1 2 3 4” and press Enter twice (the blank line terminates input) [1; 2; 3; 4] c(1,2,3,4) (R does not distinguish between row and column vectors.) v(3) A(2,3) To enter values by row: matrix(c(1,2,3,4,5,6), nrow=2, byrow=TRUE) To enter values by column: matrix(c(1,4,2,5,3,6), nrow=2) v[3] A[2,3] A(5) A[5] 2:7 7:-1:2 2:3:14 2:7 7:2 seq(2,14,3) [1 2 3 ; 4 5 6] D. Hiebeler, Matlab / R Reference No. 15 4 Description Build a vector containing n equally-spaced values between a and b inclusive Build a vector containing n logarithmically equallyspaced values between 10a and 10b inclusive Build a vector of length k containing all zeros Build a vector of length k containing the value j in all positions Build an m×n matrix of zeros Matlab linspace(a,b,n) R seq(a,b,length.out=n) seq(a,b,len=n) logspace(a,b,n) 10^seq(a,b,len=n) zeros(k,1) (for a column vector) or zeros(1,k) (for a row vector) j*ones(k,1) (for a column vector) or j*ones(1,k) (for a row vector) rep(0,k) zeros(m,n) j*ones(m,n) v=diag(A) [a1 a2] cbind(a1,a2) [a1; a2] rbind(a1,a2) 28 Build an m × n matrix containing j in all positions n × n identity matrix In Build diagonal matrix A using elements of vector v as diagonal entries Extract diagonal elements of matrix A “Glue” two matrices a1 and a2 (with the same number of rows) side-by-side “Stack” two matrices a1 and a2 (with the same number of columns) on top of each other Given vectors x and y of lengths m and n respectively, build n×m matrices X whose rows are copies of x and Y whose columns are copies of y Reverse the order of elements in vector v Column 2 of matrix A matrix(0,nrow=m,ncol=n) or just matrix(0,m,n) matrix(j,nrow=m,ncol=n) or just matrix(j,m,n) diag(n) diag(v,nrow=length(v)) (Note: if you are sure the length of vector v is 2 or more, you can simply say diag(v).) v=diag(A) 29 Row 7 of matrix A A(7,:) 30 All elements of A as a vector, column-by-column Rows 2–4, columns 6–10 of A (this is a 3 × 5 matrix) A 3 × 2 matrix consisting of rows 7, 7, and 6 and columns 2 and 1 of A (in that order) Circularly shift the rows of matrix A down by s1 elements, and right by s2 elements 16 17 18 19 20 21 22 23 24 25 26 27 31 32 33 eye(n) diag(v) or just rep(j,k) [X,Y]=meshgrid(x,y) m=length(x); n=length(y); X=matrix(rep(x,each=n),nrow=n); Y=matrix(rep(y,m),nrow=n) v(end:-1:1) rev(v) A(:,2) A(:) (gives a column vector) A[,2] Note: that gives the result as a vector. To make the result a m×1 matrix instead, do A[,2,drop=FALSE] A[7,] Note: that gives the result as a vector. To make the result a 1×n matrix instead, do A[7,,drop=FALSE] c(A) A(2:4,6:10) A[2:4,6:10] A([7 7 6], [2 1]) A[c(7,7,6),c(2,1)] circshift(A, [s1 s2]) No simple way, but modulo arithmetic on indices will work: m=dim(A)[1]; n=dim(A)[2]; A[(1:m-s1-1)%%m+1, (1:n-s2-1)%%n+1] D. Hiebeler, Matlab / R Reference No. 34 35 36 37 38 39 40 41 42 43 44 45 46 47 5 Description Flip the order of elements in each row of matrix A Flip the order of elements in each column of matrix A Given a single index ind into an m × n matrix A, compute the row r and column c of that position (also works if ind is a vector) Given the row r and column c of an element of an m × n matrix A, compute the single index ind which can be used to access that element of A (also works if r and c are vectors) Given equal-sized vectors r and c (each of length k), set elements in rows (given by r) and columns (given by c) of matrix A equal to 12. That is, k elements of A will be modified. Truncate vector v, keeping only the first 10 elements Extract elements of vector v from position a to the end All but the k th element of vector v All but the j th and k th elements of vector v Reshape matrix A, making it an m × n matrix with elements taken columnwise from the original A (which must have mn elements) Extract the lower-triangular portion of matrix A Extract the upper-triangular portion of matrix A Enter n × n Hilbert matrix H where Hij = 1/(i + j − 1) Matlab fliplr(A) R t(apply(A,1,rev)) flipud(A) apply(A,2,rev) [r,c] = ind2sub(size(A), ind) r = ((ind-1) %% m) + 1 c = floor((ind-1) / m) + 1 ind = sub2ind(size(A), r, c) ind = (c-1)*m + r inds = sub2ind(size(A),r,c); A(inds) = 12; inds = cbind(r,c) A[inds] = 12 v = v(1:10) v(a:end) v = v[1:10], or length(v) = 10 also works v[a:length(v)] v([1:(k-1) (k+1):end]) v[-k] No simple way? Generalize the previous item A = reshape(A,m,n) v[c(-j,-k)] L = tril(A) L = A; L[upper.tri(L)]=0 U = triu(A) U = A; U[lower.tri(U)]=0 hilb(n) Enter an n-dimensional array, e.g. a 3 × 4 × 2 array with the values 1 through 24 reshape(1:24, 3, 4, 2) reshape(1:24, [3 4 2]) Hilbert(n), but this is part of the Matrix package which you’ll need to install (see item 331 for how to install/load packages). array(1:24, c(3,4,2)) (Note that a matrix is 2-D, i.e. rows and columns, while an array is more generally N -D) or dim(A) = c(m,n) D. Hiebeler, Matlab / R Reference 2.1 No. 48 50 Then you v[[1]] = 12 v[[2]] = ’hi there’ v[[3]] = matrix(runif(9),3) w = v[[i]] Set the name of the ith element in a list. If you use regular indexing, i.e. w = v(i), then w will be a 1 × 1 cell matrix containing the contents of the ith element of v. (Matlab does not have names associated with elements of cell arrays.) If you use regular indexing, i.e. w = v[i], then w will be a list of length 1 containing the contents of the ith element of v. names(v)[3] = ’myrandmatrix’ Use names(v) to see all names, and names(v)=NULL to clear all names. Structs and data frames Description Matlab R Create a matrix-like object avals=2*ones(1,6); v=c(1,5,3,2,3,7); d=data.frame( with different named columns yvals=6:-1:1; v=[1 5 3 2 3 7]; cbind(a=2, yy=6:1), v) (a struct in Matlab, or a d=struct(’a’,avals, data frame in R) ’yy’, yyvals, ’fac’, v); Note that I (surprisingly) don’t use R for statistics, and therefore have very little experience with data frames (and also very little with Matlab structs). I will try to add more to this section later on. Computations 3.1 56 57 58 59 60 61 62 v{1} = 12 v{2} = ’hi there’ v{3} = rand(3) R v = vector(’list’,n) can do e.g.: w = v{i} 3 No. 52 53 54 55 Matlab v = cell(1,n) In general, cell(m,n) makes an m × n cell array. Then you can do e.g.: Extract the ith element of a cell/list vector v 2.2 No. 51 Cell arrays and lists Description Build a vector v of length n, capable of containing different data types in different elements (called a cell array in Matlab, and a list in R) 49 6 Basic computations Description a + b, a − b, ab, a/b √ a ab |a| (note: for complex arguments, this computes the modulus) ea ln(a) log2 (a), log10 (a) sin(a), cos(a), tan(a) sin−1 (a), cos−1 (a), tan−1 (a) sinh(a), cosh(a), tanh(a) sinh−1 (a), cosh−1 (a), −1 tanh (a) Matlab a+b, a-b, a*b, a/b sqrt(a) a^b abs(a) R a+b, a-b, a*b, a/b sqrt(a) a^b abs(a) exp(a) log(a) log2(a), log10(a) sin(a), cos(a), tan(a) asin(a), acos(a), atan(a) sinh(a), cosh(a), tanh(a) asinh(a), acosh(a), atanh(a) exp(a) log(a) log2(a), log10(a) sin(a), cos(a), tan(a) asin(a), acos(a), atan(a) sinh(a), cosh(a), tanh(a) asinh(a), acosh(a), atanh(a) D. Hiebeler, Matlab / R Reference No. 63 64 65 66 67 68 69 70 71 7 Description n MOD k (modulo arithmetic) Round to nearest integer Matlab mod(n,k) R n %% k round(x) Round down to next lowest integer Round up to next largest integer Sign of x (+1, 0, or -1) floor(x) round(x) (Note: R uses IEC 60559 standard, rounding 5 to the even digit — so e.g. round(0.5) gives 0, not 1.) floor(x) ceil(x) ceiling(x) sign(x) (Note: for complex values, this computes x/abs(x).) erf(x) sign(x) (Does not work with complex values) 2*pnorm(x*sqrt(2))-1 erfc(x) 2*pnorm(x*sqrt(2),lower=FALSE) Error function erf(x) √ Rx 2 (2/ π) 0 e−t dt = Complementary error function cerf(x) = √ R∞ 2 (2/ π) x e−t dt = 1-erf(x) Inverse error function erfinv(x) qnorm((1+x)/2)/sqrt(2) Inverse complementary error erfcinv(x) qnorm(x/2,lower=FALSE)/sqrt(2) function 72 Binomial coefficient nchoosek(n,k) choose(n,k) ¶ µ n = n!/(n!(n − k)!) k Note: the various functions above (logarithm, exponential, trig, abs, and rounding functions) all work with vectors and matrices, applying the function to each element, as well as with scalars. 3.2 No. 73 74 75 76 77 78 Complex numbers Description Enter a complex number Modulus (magnitude) Argument (angle) Complex conjugate Real part of z Imaginary part of z Matlab 1+2i abs(z) angle(z) conj(z) real(z) imag(z) R 1+2i abs(z) or Mod(z) Arg(z) Conj(z) Re(z) Im(z) D. Hiebeler, Matlab / R Reference 3.3 No. 79 8 Matrix/vector computations Description Vector dot product ~x · ~y = ~xT ~y Vector cross product ~x × ~y Matlab dot(x,y) R sum(x*y) cross(x,y) A * B A .* B 83 Matrix multiplication AB Element-by-element multiplication of A and B Transpose of a matrix, AT Not in base R, but e.g. the xprod function from the RSEIS package will do it (see item 331 for how to install/load packages) A %*% B A * B 84 Solve A~x = ~b 85 86 87 88 89 90 Reduced echelon form of A Determinant of A Inverse of A Trace of A Compute AB −1 Element-by-element division of A and B Compute A−1 B Square the matrix A Raise matrix A to the k th power 80 81 82 91 92 93 94 95 96 97 Raise each element of A to the k th power Rank of matrix A Set w to be a vector of eigenvalues of A, and V a matrix containing the corresponding eigenvectors Permuted LU factorization of a matrix A’ (This is actually the complex conjugate (i.e. Hermitian) transpose; use A.’ for the non-conjugate transpose if you like; they are equivalent for real matrices.) A\b Warning: if there is no solution, Matlab gives you a least-squares “best fit.” If there are many solutions, Matlab just gives you one of them. rref(A) det(A) inv(A) trace(A) A/B A ./ B t(A) for transpose, or Conj(t(A)) for conjugate (Hermitian) transpose A\B A^2 A^k solve(A,B) A %*% A (No easy way to do this in R other than repeated multiplication A %*% A %*% A...) A^k A.^k solve(A,b) Warning: this only works with square invertible matrices. R does not have a function to do this det(A) solve(A) sum(diag(A)) A %*% solve(B) A / B rank(A) [V,D]=eig(A) and then w=diag(D) since Matlab returns the eigenvalues on the diagonal of D qr(A)$rank tmp=eigen(A); w=tmp$values; V=tmp$vectors [L,U,P]=lu(A) then the matrices satisfy P A = LU . Note that this works even with non-square matrices tmp=expand(lu(Matrix(A))); L=tmp$L; U=tmp$U; P=tmp$P then the matrices satisfy A = P LU , i.e. P −1 A = LU . Note that the lu and expand functions are part of the Matrix package (see item 331 for how to install/load packages). Also note that this doesn’t seem to work correctly with non-square matrices. L, U, and P will be of class Matrix rather than class matrix; to make them the latter, instead do L=as.matrix(tmp$L), U=as.matrix(tmp$U), and P=as.matrix(tmp$P) above. D. Hiebeler, Matlab / R Reference No. 98 9 Description Singular-value decomposition: given m × n matrix A with rank r, find m × r matrix P with orthonormal columns, diagonal r × r matrix S, and r × n matrix QT with orthonormal rows so that P SQT = A Schur decomposition of square matrix, A = QT QH = QT Q−1 where Q is unitary (i.e. QH Q = I) and T is upper triangular; QH = QT is the Hermitian (conjugate) transpose Matlab [P,S,Q]=svd(A,’econ’) R tmp=svd(A); U=tmp$u; V=tmp$v; S=diag(tmp$d) [Q,T]=schur(A) Cholesky factorization of a square, symmetric, positive definite matrix A = RT R, where R is upper-triangular QR factorization of matrix A, where Q is orthogonal (satisfying QQT = I) and R is upper-triangular R = chol(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. R = chol(A) Note that chol is part of the Matrix package (see item 331 for how to install/load packages). 102 Vector norms norm(v,1) for 1-norm k~v k1 , norm(v,2) for Euclidean norm k~v k2 , norm(v,inf) for infinity-norm k~v k∞ , and norm(v,p) for p-norm P 1/p k~v kp = ( |vi |p ) 103 Matrix norms 104 Condition number cond(A) = kAk1 kA−1 k1 of A, using 1norm 105 Condition number cond(A) = kAk2 kA−1 k2 of A, using 2norm Condition number cond(A) = kAk∞ kA−1 k∞ of A, using infinity-norm norm(A,1) for 1-norm kAk1 , norm(A) for 2-norm kAk2 , norm(A,inf) for infinity-norm kAk∞ , and norm(A,’fro’) for ¡P T ¢1/2 Frobenius norm i (A A)ii cond(A,1) (Note: Matlab also has a function rcond(A) which computes reciprocal condition estimator using the 1-norm) cond(A,2) 99 100 101 106 [Q,R]=qr(A) satisfying QR = A, or [Q,R,E]=qr(A) to do permuted QR factorization satisfying AE = QR cond(A,inf) z=qr(A); Q=qr.Q(z); R=qr.R(z); E=diag(n)[,z$pivot] (where n is the number of columns in A) gives permuted QR factorization satisfying AE = QR R does not have a norm function for vectors; only one for matrices. But the following will work: norm(matrix(v),’1’) for 1-norm k~v k1 , norm(matrix(v),’i’) for infinity-norm k~v k∞ , and sum(abs(v)^p)^(1/p) for p-norm P 1/p k~v kp = ( |vi |p ) norm(A,’1’) for 1-norm kAk1 , max(svd(A)$d) for 2-norm kAk2 , norm(A,’i’) for infinity-norm kAk∞ , and norm(A,’f’) for Frobenius norm ¡P T ¢1/2 i (A A)ii 1/rcond(A,’1’) kappa(A, exact=TRUE) (leave out the “exact=TRUE” for an estimate) 1/rcond(A,’I’) D. Hiebeler, Matlab / R Reference No. 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 Description Compute mean of all elements in vector or matrix Compute means of columns of a matrix Compute means of rows of a matrix Compute standard deviation of all elements in vector or matrix Compute standard deviations of columns of a matrix Compute standard deviations of rows of a matrix Compute variance of all elements in vector or matrix Compute variance of columns of a matrix Compute variance of rows of a matrix Compute covariance for two vectors of observations Compute covariance matrix, giving covariances between columns of matrix A Given matrices A and B, build covariance matrix C where cij is the covariance between column i of A and column j of B Compute Pearson’s linear correlation coefficient between elements of vectors v and w Compute Kendall’s tau correlation statistic for vectors v and w Compute Spearman’s rho correlation statistic for vectors v and w Compute pairwise Pearson’s correlation coefficient between columns of matrix A Compute matrix C of pairwise Pearson’s correlation coefficients between each pair of columns of matrices A and B, i.e. so cij is the correlation between column i of A and column j of B 10 Matlab mean(v) for vectors, mean(A(:)) for matrices mean(A) R mean(v) or mean(A) mean(A,2) rowMeans(A) std(v) for vectors, std(A(:)) for matrices. This normalizes by n − 1. Use std(v,1) to normalize by n. std(A). This normalizes by n − 1. Use std(A,1) to normalize by n std(A,0,2) to normalize by n − 1, std(A,1,2) to normalize by n var(v) for vectors, var(A(:)) for matrices. This normalizes by n − 1. Use var(v,1) to normalize by n. var(A). This normalizes by n − 1. Use var(A,1) to normalize by n var(A,0,2) to normalize by n − 1, var(A,1,2) to normalize by n cov(v,w) computes the 2 × 2 covariance matrix; the off-diagonal elements give the desired covariance cov(A) sd(v) for vectors, sd(c(A)) for matrices. This normalizes by n − 1. colMeans(A) sd(A). This normalizes by n − 1. apply(A,1,sd). This normalizes by n − 1. var(v) for vectors, var(c(A)) for matrices. This normalizes by n − 1. apply(A,2,var). This normalizes by n − 1. apply(A,1,var). This normalizes by n − 1. cov(v,w) var(A) or cov(A) 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) 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(:)) corr(v,w,’type’,’kendall’) cor(v,w) corr(v,w,’type’,’spearman’) cor(v,w,method=’spearman’) 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 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 cor(v,w,method=’kendall’) D. Hiebeler, Matlab / R Reference No. 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 Description Compute sum of all elements in vector or matrix Compute sums of columns of matrix Compute sums of rows of matrix Compute product of all elements in vector or matrix Compute products of columns of matrix Compute products of rows of matrix Compute P∞ matrix exponential eA = k=0 Ak /k! Compute cumulative sum of values in vector Compute cumulative sums of columns of matrix Compute cumulative sums of rows of matrix Compute cumulative sum of all elements of matrix (column-by-column) Cumulative product of elements in vector v Cumulative minimum or maximum of elements in vector v Compute differences between consecutive elements of vector v. Result is a vector w 1 element shorter than v, where element i of w is element i + 1 of v minus element i of v Make a vector y the same size as vector x, which equals 4 everywhere that x is greater than 5, and equals 3 everywhere else (done via a vectorized computation). Compute minimum of values in vector v Compute minimum of all values in matrix A Compute minimum value of each column of matrix A Compute minimum value of each row of matrix A 11 Matlab sum(v) for vectors, sum(A(:)) for matrices sum(A) R sum(v) or sum(A) sum(A,2) rowSums(A) prod(v) for vectors, prod(A(:)) for matrices prod(A) prod(v) or prod(A) prod(A,2) apply(A,1,prod) expm(A) cumsum(v) expm(Matrix(A)), but this is part of the Matrix package which you’ll need to install (see item 331 for how to install/load packages). cumsum(v) cumsum(A) apply(A,2,cumsum) cumsum(A,2) t(apply(A,1,cumsum)) cumsum(A(:)) cumsum(A) cumprod(v) (Can also be used in the various ways cumsum can) I don’t know of an easy way to do this in Matlab cumprod(v) (Can also be used in the various ways cumsum can) cummin(v) or cummax(v) diff(v) diff(v) z = [3 4]; y = z((x > 5)+1) y = ifelse(x > 5, 4, 3) min(v) min(v) min(A(:)) min(A) min(A) (returns a row vector) apply(A,2,min) (returns a vector) min(A, [ ], 2) (returns a column vector) apply(A,1,min) (returns a vector) colSums(A) apply(A,2,prod) D. Hiebeler, Matlab / R Reference No. 143 144 145 146 Description Given matrices A and B, compute a matrix where each element is the minimum of the corresponding elements of A and B Given matrix A and scalar c, compute a matrix where each element is the minimum of c and the corresponding element of A Find minimum among all values in matrices A and B Find index of the first time min(v) appears in v, and store that index in ind Notes: 12 Matlab min(A,B) R pmin(A,B) min(A,c) pmin(A,c) min([A(:) ; B(:)]) [y,ind] = min(v) min(A,B) ind = which.min(v) • Matlab and R both have a max function (and R has pmax and which.max as well) which behaves in the same ways as min but to compute maxima rather than minima. • Functions like exp, sin, sqrt etc. will operate on arrays in both Matlab and R, doing the computations for each element of the matrix. No. 147 148 149 150 151 152 153 154 155 156 Description Number of rows in A Number of columns in A Dimensions of A, listed in a vector Number of elements in vector v Total number of elements in matrix A Max. dimension of A Sort values in vector v Sort values in v, putting sorted values in s, and indices in idx, in the sense that s[k] = x[idx[k]] Sort the order of the rows of matrix m Matlab size(A,1) size(A,2) size(A) R nrow(A) ncol(A) dim(A) length(v) length(v) numel(A) length(A) length(A) sort(v) [s,idx]=sort(v) max(dim(A)) sort(v) tmp=sort(v,index.return=TRUE); s=tmp$x; idx=tmp$ix sortrows(m) This sorts according to the first column, then uses column 2 to break ties, then column 3 for remaining ties, etc. Complex numbers are sorted by abs(x), and ties are then broken by angle(x). Sort order of rows of matrix m, specifying to use columns c1, c2, c3 as the sorting “keys” sortrows(m, [c1 c2 c2]) m[order(m[,1]),] This only sorts according to the first column. To use column 2 to break ties, and then column 3 to break further ties, do m[order(m[,1], m[,2], m[,3]),] Complex numbers are sorted first by real part, then by imaginary part. m[order(m[,c1], m[,c2], m[,c3]),] D. Hiebeler, Matlab / R Reference No. 157 158 159 160 161 162 163 164 165 Description Same as previous item, but sort in decreasing order for columns c1 and c2 Sort order of rows of matrix m, and keep indices used for sorting To count how many values in the vector v are between 4 and 7 (inclusive on the upper end) Given vector v, return list of indices of elements of v which are greater than 5 Given matrix A, return list of indices of elements of A which are greater than 5, using single-indexing Given matrix A, generate vectors r and c giving rows and columns of elements of A which are greater than 5 Given vector x (of presumably discrete values), build a vector v listing unique values in x, and corresponding vector c indicating how many times those values appear in x Given vector x (of presumably continuous values), divide the range of values into k equally-sized bins, and build a vector m containing the midpoints of the bins and a corresponding vector c containing the counts of values in the bins Convolution / polynomial multiplication (given vectors x and y containing polynomial coefficients, their convolution is a vector containing coefficients of the product of the two polynomials) 13 Matlab sortrows(m, [-c1 -c2 c2]) R m[order(-m[,c1], -m[,c2], m[,c3]),] [y,i] = sortrows(m) i=order(m[1,]); y=m[i,] sum((v > 4) & (v <= 7)) sum((v > 4) & (v <= 7)) find(v > 5) which(v > 5) find(A > 5) which(A > 5) [r,c] = find(A > 5) w = which(A > 5, arr.ind=TRUE); r=w[,1]; c=w[,2] v = unique(x); c = hist(x,v); w=table(x); c=as.numeric(w); v=as.numeric(names(w)) [c,m] = hist(x,k) w=hist(x,seq(min(x),max(x), length.out=k+1), plot=FALSE); m=w$mids; c=w$counts conv(x,y) convolve(x,rev(y),type=’open’) Note: the accuracy of this is not as good as Matlab; e.g. doing v=c(1,-1); for (i in 2:20) v=convolve(v,c(-i,1), type=’open’) to generate the 20th -degree Q20 Wilkinson polynomial W (x) = i=1 (x−i) gives a coefficient of ≈ −780.19 for x19 , rather than the correct value -210. D. Hiebeler, Matlab / R Reference 3.4 No. 166 167 No. 168 169 170 171 Root-finding Description Find roots of polynomial whose coefficients are stored in vector v (coefficients in v are highest-order first) Find zero (root) of a function f (x) of one variable 3.5 14 Matlab roots(v) Define function f(x), then do fzero(f,x0) to search for a root near x0, or fzero(f,[a b]) to find a root between a and b, assuming the sign of f (x) differs at x = a and x = b. Default forward error tolerance (i.e. error in x) is machine epsilon ǫmach . R polyroot(rev(v)) (This function really wants the vector to have the constant coefficient first in v; rev reverses their order to achieve this.) Define function f(x), then do uniroot(f, c(a,b)) to find a root between a and b, assuming the sign of f (x) differs at x = a and x = b. Default forward error tolerance (i.e. error in x) is fourth root of machine epsilon, (ǫmach )0.25 . To specify e.g. a tolerance of 2−52 , do uniroot(f, c(a,b), tol=2^-52). Function optimization/minimization Description Find value m which minimizes a function f (x) of one variable within the interval from a to b Find value m which minimizes a function f (x, p1 , p2 ) with given extra parameters (but minimization is only occuring over the first argument), in the interval from a to b. Find values of x, y, z which minimize function f (x, y, z), using a starting guess of x = 1, y = 2.2, and z = 3.4. Find values of x, y, z which minimize function f (x, y, z, p1 , p2 ), using a starting guess of x = 1, y = 2.2, and z = 3.4, where the function takes some extra parameters (useful e.g. for doing things like nonlinear least-squares optimization where you pass in some data vectors as extra parameters). Matlab Define function f(x), then do R Define function f(x), then do m = fminbnd(f, a, b) m = optimize(f,c(a,b))$minimum Define function f(x,p1,p2), then use an “anonymous function”: Define function f(x,p1,p2), then: % first define values for p1 % and p2, and then do: m=fminbnd(@(x) f(x,p1,p2),a,b) # first define values for p1 # and p2, and then do: m = optimize(f, c(a,b), p1=p1, p2=p2)$minimum First write function f(v) which accepts a vector argument v containing values of x, y, and z, and returns the scalar value f (x, y, z), then do: First write function f(v) which accepts a vector argument v containing values of x, y, and z, and returns the scalar value f (x, y, z), then do: fminsearch(@f,[1 2.2 3.4]) optim(c(1,2.2,3.4),f)$par First write function f(v,p1,p2) which accepts a vector argument v containing values of x, y, and z, along with the extra parameters, and returns the scalar value f (x, y, z, p1 , p2 ), then do: First write function f(v,p1,p2) which accepts a vector argument v containing values of x, y, and z, along with the extra parameters, and returns the scalar value f (x, y, z, p1 , p2 ), then do: fminsearch(@f,[1 2.2 3.4], ... [ ], p1, p2) Or use an anonymous function: fminsearch(@(x) f(x,p1,p2), ... [1 2.2 3.4]) optim(c(1,2.2,3.4), f, p1=p1, p2=p2)$par D. Hiebeler, Matlab / R Reference 3.6 15 Numerical integration / quadrature No. 172 Description Numerically integrate function f (x) over interval from a to b Matlab quad(f,a,b) uses son’s quadrature, absolute tolerance specify absolute quad(f,a,b,tol) 173 Simple trapezoidal numerical integration using (x, y) values in vectors x and y trapz(x,y) adaptive Simpwith a default of 10−6 . To tolerance, use R integrate(f,a,b) uses adaptive quadrature with default absolute and relative error tolerances being the fourth root of machine epsilon, (ǫmach )0.25 ≈ 1.22 × 10−4 . Tolerances can be specified by using integrate(f,a,b, rel.tol=tol1, abs.tol=tol2). Note that the function f must be written to work even when given a vector of x values as its argument. sum(diff(x)*(y[-length(y)]+ y[-1])/2) D. Hiebeler, Matlab / R Reference 3.7 No. 174 175 176 177 178 179 16 Curve fitting Description Fit the line y = c1 x + c0 to data in vectors x and y. Fit the quadratic polynomial y = c2 x2 + c1 x + c0 to data in vectors x and y. Fit nth degree polynomial y = cn xn + cn−1 xn−1 + . . . + c1 x + c0 to data in vectors x and y. Fit the quadratic polynomial with zero intercept, y = c2 x2 + c1 x to data in vectors x and y. Fit natural cubic spline (S ′′ (x) = 0 at both endpoints) to points (xi , yi ) whose coordinates are in vectors x and y; evaluate at points whose x coordinates are in vector xx, storing corresponding y’s in yy Fit cubic spline using Forsythe, Malcolm and Moler method (third derivatives at endpoints match third derivatives of exact cubics through the four points at each end) to points (xi , yi ) whose coordinates are in vectors x and y; evaluate at points whose x coordinates are in vector xx, storing corresponding y’s in yy Matlab R p = polyfit(x,y,1) p = coef(lm(y ~ x)) The return vector p has the coefficients in descending order, i.e. p(1) is c1 , and p(2) is c0 . The return vector p has the coefficients in ascending order, i.e. p[1] is c0 , and p[2] is c1 . p = polyfit(x,y,2) p = coef(lm(y ~ x + I(x^2))) The return vector p has the coefficients in descending order, i.e. p(1) is c2 , p(2) is c1 , and p(3) is c0 . The return vector p has the coefficients in ascending order, i.e. p[1] is c0 , p[2] is c1 , and p[3] is c2 . No simple built-in way. But this will work: coef(lm(as.formula(paste( ’y~’,paste(’I(x^’,1:n,’)’, sep=’’,collapse=’+’))))) This more concise “lowerlevel” method will also work: coef(lm.fit(outer(x,0:n,’^’),y)) Note that both of the above return the coefficients in ascending order. Also see the polyreg function in the mda package (see item 331 for how to install/load packages). p = polyfit(x,y,n) The return vector p has the coefficients in descending order, p(1) is cn , p(2) is cn−1 , etc. (I don’t know a simple way do this in Matlab, other than to write a function which computes the sum of squared residuals and use fminsearch on that function. There is likely an easy way to do it in the Statistics Toolbox.) pp=csape(x,y,’variational’); yy=ppval(pp,xx) but note that csape is in Matlab’s Spline Toolbox I’m not aware of a function to do this in Matlab p=coef(lm(y ~ -1 + x + I(x^2))) The return vector p has the coefficients in ascending order, i.e. p[1] is c1 , and p[2] is c2 . tmp=spline(x,y,method=’natural’, xout=xx); yy=tmp$y tmp=spline(x,y,xout=xx); yy=tmp$y D. Hiebeler, Matlab / R Reference No. 180 Description Fit cubic spline such that first derivatives at endpoints match first derivatives of exact cubics through the four points at each end) to points (xi , yi ) whose coordinates are in vectors x and y; evaluate at points whose x coordinates are in vector xx, storing corresponding y’s in yy Fit cubic spline with periodic boundaries, i.e. so that first and second derivatives match at the left and right ends (the first and last y values of the provided data should also agree), to points (xi , yi ) whose coordinates are in vectors x and y; evaluate at points whose x coordinates are in vector xx, storing corresponding y’s in yy Fit cubic spline with “nota-knot” conditions (the first two piecewise cubics coincide, as do the last two), to points (xi , yi ) whose coordinates are in vectors x and y; evaluate at points whose x coordinates are in vector xx, storing corresponding y’s in yy 181 182 4 No. 183 17 Matlab pp=csape(x,y); yy=ppval(pp,xx) but csape is in Matlab’s Spline Toolbox R I’m not aware of a function to do this in R pp=csape(x,y,’periodic’); yy=ppval(pp,xx) but csape is in Matlab’s Spline Toolbox tmp=spline(x,y,method= ’periodic’, xout=xx); yy=tmp$y yy=spline(x,y,xx) I’m not aware of a function to do this in R Conditionals, control structure, loops Description “for” loops over values in a vector v (the vector v is often constructed via a:b) Matlab R If only one command inside the loop: for i=v command1 command2 end for (i in v) command or for (i in v) command If multiple commands inside the loop: for (i in v) { command1 command2 } D. Hiebeler, Matlab / R Reference No. 184 Description “if” statements with no else clause 18 Matlab R If only one command inside the clause: if cond command1 command2 end if (cond) command or if (cond) command If multiple commands: if (cond) { command1 command2 } 185 “if/else” statement If one command in clauses: if cond command1 command2 else command3 command4 end Note: Matlab also has an “elseif” statement, e.g.: if cond1 command1 elseif cond2 command2 elseif cond3 command3 else command4 end if (cond) command1 else command2 or if (cond) cmd1 else cmd2 If multiple commands: if (cond) { command1 command2 } else { command3 command4 } Warning: the “else” must be on the same line as command1 or the “}” (when typed interactively at the command prompt), otherwise R thinks the “if” statement was finished and gives an error. R does not have an “elseif” statement. Logical comparisons which can be used on scalars in “if” statements, or which operate element-byelement on vectors/matrices: Matlab xa x <= a x >= a x == a x ~= a R x x x x x x a <= a >= a == a != a Description True if x is less than a True if x is greater than a True if x is less than or equal to a True if x is greater than or equal to a True if x is equal to a True if x is not equal to a D. Hiebeler, Matlab / R Reference 19 Scalar logical operators: Description a AND b a OR b a XOR b NOT a Matlab a && b a || b xor(a,b) ~a R a && b a || b xor(a,b) !a The && and || operators are short-circuiting, i.e. && stops as soon as any of its terms are FALSE, and || stops as soon as any of its terms are TRUE. Matrix logical operators (they operate element-by-element): Description a AND b a OR b a XOR b NOT a No. 186 187 188 189 Description To test whether a scalar value x is between 4 and 7 (inclusive on the upper end) To count how many values in the vector x are between 4 and 7 (inclusive on the upper end) Test whether all values in a logical/boolean vector are TRUE Test whether any values in a logical/boolean vector are TRUE Matlab a & b a | b xor(a,b) ~a R a & b a | b xor(a,b) !a Matlab if ((x > 4) && (x <= 7)) R if ((x > 4) && (x <= 7)) sum((x > 4) & (x <= 7)) sum((x > 4) & (x <= 7)) all(v) all(v) any(v) any(v) D. Hiebeler, Matlab / R Reference No. 190 191 192 Description “while” statements to do iteration (useful when you don’t know ahead of time how many iterations you’ll need). E.g. to add uniform random numbers between 0 and 1 (and their squares) until their sum is greater than 20: More flow control: these commands exit or move on to the next iteration of the innermost while or for loop, respectively. “Switch” statements for integers 20 Matlab R mysum = 0; mysumsqr = 0; while (mysum < 20) r = rand; mysum = mysum + r; mysumsqr = mysumsqr + r^2; end mysum = 0 mysumsqr = 0 while (mysum < 20) { r = runif(1) mysum = mysum + r mysumsqr = mysumsqr + r^2 } break and continue (As with “if” statements and “for” loops, the curly brackets are not necessary if there’s only one statement inside the “while” loop.) break and next switch (x) case 10 disp(’ten’) case {12,13} disp(’dozen (bakers?)’) otherwise disp(’unrecognized’) end R doesn’t have a switch statement capable of doing this. It has a function which is fairly limited for integers, but can which do string matching. See ?switch for more. But a basic example of what it can do for integers is below, showing that you can use it to return different expressions based on whether a value is 1, 2, . . .. mystr = switch(x, ’one’, ’two’, ’three’); print(mystr) Note that switch returns NULL if x is larger than 3 in the above case. Also, continuous values of x will be truncated to integers. D. Hiebeler, Matlab / R Reference 5 No. 193 Functions, ODEs Description Implement add(x,y) a function Matlab Put the following in add.m: function retval=add(x,y) retval = x+y; Then you can do e.g. add(2,3) 194 21 Implement a function f(x,y,z) which returns multiple values, and store those return values in variables u and v Write function as follows: function [a,b] = f(x,y,z) a = x*y+z; b=2*sin(x-z); Then call the function by doing: [u,v] = f(2,8,12) R Enter the following, or put it in a file and source that file: add = function(x,y) { return(x+y) } Then you can do e.g. add(2,3). Note, the curly brackets aren’t needed if your function only has one line. Also, the return keyword is optional in the above example, as the value of the last expression in a function gets returned, so just x+y would work too. Write function as follows: f = function(x,y,z) { a = x*y+z; b=2*sin(x-z) return(list(a,b)) } Then call the function by doing: tmp=f(2,8,12); u=tmp[[1]]; v=tmp[[2]]. The above is most general, and will work even when u and v are different types of data. If they are both scalars, the function could simply return them packed in a vector, i.e. return(c(a,b)). If they are vectors of the same size, the function could return them packed together into the columns of a matrix, i.e. return(cbind(a,b)). D. Hiebeler, Matlab / R Reference No. 195 196 197 Description Numerically solve ODE dx/dt = 5x from t = 3 to t = 12 with initial condition x(3) = 7 Numerically solve system of ODEs dw/dt = 5w, dz/dt = 3w + 7z from t = 3 to t = 12 with initial conditions w(3) = 7, z(3) = 8.2 Pass parameters such as r = 1.3 and K = 50 to an ODE function from the command line, solving dx/dt = rx(1 − x/K) from t = 0 to t = 20 with initial condition x(0) = 2.5. 22 Matlab First implement function R First implement function function retval=f(t,x) retval = 5*x; f = function(t,x,parms) { return(list(5*x)) } Then do ode45(@f,[3,12],7) to plot solution, or [t,x]=ode45(@f,[3,12],7) to get back vector t containing time values and vector x containing corresponding function values. If you want function values at specific times, e.g. 3, 3.1, 3.2, . . . , 11.9, 12, you can do [t,x]=ode45(@f,3:0.1:12,7). Note: in older versions of Matlab, use ’f’ instead of @f. First implement function function retval=myfunc(t,x) w = x(1); z = x(2); retval = zeros(2,1); retval(1) = 5*w; retval(2) = 3*w + 7*z; Then do ode45(@myfunc,[3,12],[7; 8.2]) to plot solution, or [t,x]=ode45(@myfunc,[3,12],[7; 8.2]) to get back vector t containing time values and matrix x, whose first column containing corresponding w(t) values and second column contains z(t) values. If you want function values at specific times, e.g. 3, 3.1, 3.2, . . . , 11.9, 12, you can do [t,x]=ode45(@myfunc,3:0.1:12,[7; 8.2]). Note: in older versions of Matlab, use ’f’ instead of @f. First implement function function retval=func2(t,x,r,K) retval = r*x*(1-x/K) Then do ode45(@func2,[0 20], 2.5, [ ], 1.3, 50). The empty matrix is necessary between the initial condition and the beginning of your extra parameters. Then do y=lsoda(7, seq(3,12, 0.1), f,NA) to obtain solution values at times 3, 3.1, 3.2, . . . , 11.9, 12. The first column of y, namely y[,1] contains the time values; the second column y[,2] contains the corresponding function values. Note: lsoda is part of the deSolve package (see item 331 for how to install/load packages). First implement function myfunc = function(t,x,parms) { w = x[1]; z = x[2]; return(list(c(5*w, 3*w+7*z))) } Then do y=lsoda(c(7,8.2), seq(3,12, 0.1), myfunc,NA) to obtain solution values at times 3, 3.1, 3.2, . . . , 11.9, 12. The first column of y, namely y[,1] contains the time values; the second column y[,2] contains the corresponding values of w(t); and the third column contains z(t). Note: lsoda is part of the deSolve package (see item 331 for how to install/load packages). First implement function func2=function(t,x,parms) { r=parms[1]; K=parms[2] return(list(r*x*(1-x/K))) } Then do y=lsoda(2.5,seq(0,20,0.1), func2,c(1.3,50)) Note: lsoda is part of the deSolve package (see item 331 for how to install/load packages). D. Hiebeler, Matlab / R Reference 6 No. 198 199 200 201 202 203 204 205 206 207 208 209 210 23 Probability and random values Description Generate a continuous uniform random value between 0 and 1 Generate vector of n uniform random vals between 0 and 1 Generate m×n matrix of uniform random values between 0 and 1 Generate m×n matrix of continuous uniform random values between a and b Generate a random integer between 1 and k Matlab rand R runif(1) rand(n,1) or rand(1,n) runif(n) rand(m,n) matrix(runif(m*n),m,n) matrix(runif(m*n),m) a+rand(m,n)*(b-a) or if you have the Statistics toolbox then unifrnd(a,b,m,n) floor(k*rand) + 1 matrix(runif(m*n,a,b),m) Generate m×n matrix of discrete uniform random integers between 1 and k Generate m × n matrix where each entry is 1 with probability p, otherwise is 0 floor(k*rand(m,n))+1 or if you have the Statistics toolbox then unidrnd(k,m,n) (rand(m,n)=0)*exp(-x/mu)/mu will work even without the Statistics Toolbox, as long as mu is positive. normpdf(x,mu,sigma) or exp(-(x-mu)^2/(2*sigma^2))/ (sqrt(2*pi)*sigma) will work even without the Statistics Toolbox. R dbinom(x,n,p) unifpdf(x,a,b) or ((x>=a)&&(x<=b))/(b-a) will work even without the Statistics Toolbox. dunif(x,a,b) dpois(x,lambda) dexp(x,1/mu) dnorm(x,mu,sigma) unidpdf(x,n) or ((x==floor(x)) ((x==round(x)) && (x >= 1) && && (x>=1)&&(x<=n))/n will work (x <= n))/n even without the Statistics Toolbox, as long as n is a positive integer. 228 mnpdf(x,p) dmultinom(x,prob=p) Note: vector p must sum to one. Also, x and p can be vectors of length k, or if one or both are m × k matrices then the computations are performed for each row. Note: one or more of the parameters in the above “*pdf” (Matlab) or “d*” (R) functions can be vectors, but they must be the same size. Scalars are promoted to arrays of the appropriate size. D. Hiebeler, Matlab / R Reference No. 229 230 231 232 233 234 The corresponding CDF functions are below: Description Matlab Compute probability that a binocdf(x,n,p). Without the random variable from the Statistics Toolbox, as long Binomial(n, p) distribution is as n is a non-negative inless than or equal to x (i.e. teger, this will work: r = the cumulative distribution 0:floor(x); sum(factorial(n)./ function, or cdf). (factorial(r).*factorial(n-r)) .*p.^r.*(1-p).^(n-r)). (Unfortunately, Matlab’s nchoosek function won’t take a vector argument for k.) Compute probability that a poisscdf(x,lambda). Withrandom variable from the out the Statistics Toolbox, as Poisson(λ) distribution is less long as lambda ≥ 0, this than or equal to x. will work: r = 0:floor(x); sum(exp(-lambda)*lambda.^r ./factorial(r)) Compute cumulative distri- expcdf(x,mu) or bution function at x for a (x>=0)*(1-exp(-x/mu)) will random variable from the ex- work even without the Statistics ponential distribution with Toolbox, as long as mu is positive. mean µ. Compute cumulative distri- normcdf(x,mu,sigma) or 1/2 bution function at x for a ran- erf(-(x-mu)/(sigma*sqrt(2)))/2 dom variable from the Nor- will work even without the Statismal distribution with mean µ tics Toolbox, as long as sigma is and standard deviation σ. positive. Compute cumulative distri- unifcdf(x,a,b) or bution function at x for a ran- (x>a)*(min(x,b)-a)/(b-a) will dom variable from the contin- work even without the Statistics uous uniform distribution on Toolbox, as long as b > a. interval (a, b). Compute probability that a unidcdf(x,n) or random variable from the dis- (x>=1)*min(floor(x),n)/n will crete uniform distribution on work even without the Statistics integers 1 . . . n is less than or Toolbox, as long as n is a positive equal to x. integer. 26 R pbinom(x,n,p) ppois(x,lambda) pexp(x,1/mu) pnorm(x,mu,sigma) punif(x,a,b) (x>=1)*min(floor(x),n)/n D. Hiebeler, Matlab / R Reference 7 Graphics 7.1 Various types of plotting No. 235 Description Create a new figure window Matlab figure 236 Select figure number n figure(n) (will create the figure if it doesn’t exist) 237 gcf 238 Determine which figure window is currently active List open figure windows 239 Close figure window(s) 240 241 Plot points using open circles Plot points using solid lines 242 Plotting: color, point markers, linestyle 243 27 Plotting axes with logarithmic get(0,’children’) (The 0 handle refers to the root graphics object.) close to close the current figure window, close(n) to close a specified figure, and close all to close all figures plot(x,y,’o’) plot(x,y) plot(x,y,str) where str is a string specifying color, point marker, and/or linestyle (see table below) (e.g. ’gs--’ for green squares with dashed line) semilogx, semilogy, and loglog functions take arguments like plot, and plot with logarithmic scales for x, y, and both axes, respectively R dev.new() Notes: internally, on Windows this calls windows(), on MacOS it calls quartz(), and on Linux it calls X11(). X11() is also available on MacOS; you can tell R to use it by default by doing options(device=’X11’). In R sometime after 2.7.0, X11 graphics started doing antialising by default, which makes plots look smoother but takes longer to draw. If you are using X11 graphics in R and notice that figure plotting is extremely slow (especially if making many plots), do this before calling dev.new(): X11.options(type=’Xlib’) or X11.options(antialias=’none’). Or just use e.g. X11(type=’Xlib’) to make new figure windows. They are uglier (lines are more jagged), but render much more quickly. dev.set(n) (returns the actual device selected; will be different from n if there is no figure device with number n) dev.cur() dev.list() dev.off() to close the currently active figure device, dev.off(n) to close a specified one, and graphics.off() to close all figure devices. plot(x,y) plot(x,y,type=’l’) (Note: that’s a lower-case ’L’, not the number 1) plot(x,y,type=str1, pch=arg2,col=str3, lty=arg4) See tables below for possible values of the 4 parameters plot(..., log=’x’), plot(..., log=’y’), and plot(..., log=’xy’) plot with logarithmic scales for x, y, and both axes, respectively D. Hiebeler, Matlab / R Reference No. 244 Description Make bar graph where the x coordinates of the bars are in x, and their heights are in y 245 Make histogram of values in x Given vector x containing discrete values, make a bar graph where the x coordinates of bars are the values, and heights are the counts of how many times the values appear in x Given vector x containing continuous values, lump the data into k bins and make a histogram / bar graph of the binned data Make a plot containing errorbars of height s above and below (x, y) points 246 247 248 28 Matlab bar(x,y) Or just bar(y) if you only want to specify heights. Note: if A is a matrix, bar(A) interprets each column as a separate set of observations, and each row as a different observation within a set. So a 20 × 2 matrix is plotted as 2 sets of 20 observations, while a 2 × 20 matrix is plotted as 20 sets of 2 observations. hist(x) R Can’t do this in R; but barplot(y) makes a bar graph where you specify the heights, barplot(y,w) also specifies the widths of the bars, and hist can make plots like this too. v=unique(x); c=hist(x,v); bar(v,c) barplot(table(x)) [c,m] = hist(x,k); bar(m,c) or for slightly different plot style use hist(x,k) hist(x,seq(min(x), max(x), length.out=k+1)) errorbar(x,y,s) errbar(x,y,y+s,y-s) Note: errbar is part of the Hmisc package (see item 331 for how to install/load packages). errbar(x,y,y+a,y-b) Note: errbar is part of the Hmisc package (see item 331 for how to install/load packages). pie(v) 249 Make a plot containing errorbars of height a above and b below (x, y) points errorbar(x,y,b,a) 250 Other types of 2-D plots stem(x,y) and stairs(x,y) for other types of 2-D plots. polar(theta,r) to use polar coordinates for plotting. hist(x) D. Hiebeler, Matlab / R Reference No. 251 Description Make a 3-D plot of some data points with given x, y, z coordinates in the vectors x, y, and z. 252 Surface plot of data in matrix A 253 Surface plot √ sin(x + y) y of x between 90 values of y 8 of f (x, y) = for 100 values 0 and 10, and between 2 and 29 Matlab plot3(x,y,z) This works much like plot, as far as plotting symbols, linetypes, and colors. R cloud(z~x*y) You can also use arguments pch and col as with plot. To make a 3-D plot with lines, do cloud(z~x*y,type=’l’, panel.cloud=panel.3dwire) surf(A) persp(A) You can then click on the small curved arrow in the figure window (or choose “Rotate 3D” from the “Tools” menu), and then click and drag the mouse in the figure to rotate it in three dimensions. You can include shading in the image via e.g. persp(A,shade=0.5). There are two viewing angles you can also specify, among other parameters, e.g. persp(A, shade=0.5, theta=50, phi=35). x = linspace(0,10,100); y = linspace(2,8,90); [X,Y] = meshgrid(x,y); Z = sin(X+Y).*sqrt(Y); surf(X,Y,Z) shading flat x = seq(0,10,len=100) y = seq(2,8,len=90) f = function(x,y) return(sin(x+y)*sqrt(y)) z = outer(x,y,f) persp(x,y,z) contour(x,y,z) Or do s=expand.grid(x=x,y=y), and then wireframe(z~x*y,s) or wireframe(z~x*y,s,shade=TRUE) (Note: wireframe is part of the lattice package; see item 331 for how to load packages). If you have vectors x, y, and z all the same length, you can also do symbols(x,y,z). You have to do this when you make the plot, e.g. plot(x,y,xlim=c(x1,x2), ylim=c(y1,y2)) title(main=’somestring’) adds a main title, title(sub=’somestring’) adds a subtitle. You can also include main= and sub= arguments in a plot command. title(xlab=’somestring’, ylab=’anotherstr’). You can also include xlab= and ylab= arguments in a plot command. 254 Other ways of plotting the data from the previous command mesh(X,Y,Z), surfc(X,Y,Z), surfl(X,Y,Z), contour(X,Y,Z), pcolor(X,Y,Z), waterfall(X,Y,Z). Also see the slice command. 255 Set axis ranges in a figure window axis([x1 x2 y1 y2]) 256 Add title to plot title(’somestring’) 257 Add axis labels to plot xlabel(’somestring’) ylabel(’somestring’) and D. Hiebeler, Matlab / R Reference No. 258 Description Include Greek letters or symbols in plot axis labels 259 Change font size to 16 in plot labels 260 Add grid lines to plot grid on (and grid off to turn off) 261 262 Add a text label to a plot Add set of text labels to a plot. xv and yv are vectors. Add an arrow to current plot, with tail at (xt, yt) and head at (xh, yh) text(x,y,’hello’) s={’hi’, ’there’}; text(xv,yv,s) annotation(’arrow’, [xt xh], [yt yh]) Note: coordinates should be normalized figure coordinates, not coordinates within your displayed axes. Find and download from The Mathworks the file dsxy2figxy.m which converts for you, then do this: [fx,fy]=dsxy2figxy([xt xh], [yt yh]); annotation(’arrow’, fx, fy) annotation(’doublearrow’, [x0 x1], [y0 y1]) See note in previous item about normalized figure coordinates. legend(’first’, ’second’, ’Location’, ’NorthWest’) 263 264 Add a double-headed arrow to current plot, with coordinates (x0, y0) and (x1, y1) 265 Add figure legend to top-left corner of plot Matlab You can use basic TeX commands, e.g. plot(x,y); xlabel(’\phi^2 + \mu_{i,j}’) or xlabel(’fecundity \phi’) See also help tex and parts of doc text props for more about building labels using general LaTeX commands For the legends and numerical axis labels, use set(gca, ’FontSize’, 16), and for text labels on axes do e.g. xlabel(’my x var’, ’FontSize’, 16) 30 R plot(x,y,xlab= expression(phi^2 + mu[’i,j’])) or plot(x,y,xlab=expression( paste(’fecundity ’, phi))) See also help(plotmath) and p. 98 of the R Graphics book by Paul Murrell for more. For on-screen graphics, do par(ps=16) followed by e.g. a plot command. For PostScript or PDF plots, add a pointsize=16 argument, e.g. pdf(’myfile.pdf’, width=8, height=8, pointsize=16) (see items 275 and 276) grid() Note that if you’ll be printing the plot, the default style for grid-lines is to use gray dotted lines, which are almost invisible on some printers. You may want to do e.g. grid(lty=’dashed’, col=’black’) to use black dashed lines which are easier to see. text(x,y,’hello’) s=c(’hi’, ’there’); text(xv,yv,s) arrows(xt, yt, xh, yh) arrows(x0, y0, x1, y1, code=3) legend(’topleft’, legend=c(’first’, ’second’), col=c(’red’, ’blue’), pch=c(’*’,’o’)) Matlab note: sometimes you build a graph piece-by-piece, and then want to manually add a legend which doesn’t correspond with the order you put things in the plot. You can manually construct a legend by plotting “invisible” things, then building the legend using them. E.g. to make a legend with black stars and solid lines, and red circles and dashed lines: h1=plot(0,0,’k*-’); set(h1,’Visible’, ’off’); h2=plot(0,0,’k*-’); set(h2,’Visible’, ’off’); legend([h1 h2], ’blah, ’whoa’). Just be sure to choose coordinates for your “invisible” points within the current figure’s axis ranges. D. Hiebeler, Matlab / R Reference 31 No. 266 Description Adding more things to a figure Matlab hold on means everything plotted from now on in that figure window is added to what’s already there. hold off turns it off. clf clears the figure and turns off hold. 267 Plot multiple data sets at once 268 Plot sin(2x) for x between 7 and 18 plot(x,y) where x and y are 2-D matrices. Each column of x is plotted against the corresponding column of y. If x has only one column, it will be re-used. fplot(’sin(2*x)’, [7 18]) 269 Plot color image of integer values in matrix A image(A) to use array values as raw indices into colormap, or imagesc(A) to automatically scale values first (these both draw row 1 of the matrix at the top of the image); or pcolor(A) (draws row 1 of the matrix at the bottom of the image). After using pcolor, try the commands shading flat or shading interp. 270 Add colorbar legend to image plot colorbar, pcolor. 271 Set colormap in image colormap(hot). Instead of hot, you can also use gray, flag, jet (the default), cool, bone, copper, pink, hsv, prism. By default, the length of the new colormap is the same as the currently-installed one; use e.g. colormap(hot(256)) to specify the number of entries. after using image or R points(...) and lines(...) work like plot, but add to what’s already in the figure rather than clearing the figure first. points and lines are basically identical, just with different default plotting styles. Note: axes are not recalculated/redrawn when adding more things to a figure. matplot(x,y) where x and y are 2-D matrices. Each column of x is plotted against the corresponding column of y. If x has only one column, it will be re-used. curve(sin(2*x), 7, 18, 200) makes the plot, by sampling the value of the function at 200 values between 7 and 18 (if you don’t specify the number of points, 101 is the default). You could do this manually yourself via commands like tmpx=seq(7,18,len=200); plot(tmpx, sin(2*tmpx)). image(A) (it rotates the matrix 90 degrees counterclockwise: it draws row 1 of A as the left column of the image, and column 1 of A as the bottom row of the image, so the row number is the x coord and column number is the y coord). It also rescales colors. If you are using a colormap with k entries, but the value k does not appear in A, use image(A,zlim=c(1,k)) to avoid rescaling of colors. Or e.g. image(A,zlim=c(0,k-1)) if you want values 0 through k−1 to be plotted using the k colors. Use filled.contour(A) rather than image(A), although it “blurs” the data via interpolation, or use levelplot(A) from the lattice package (see item 331 for how to load packages). To use a colormap with the latter, do e.g. levelplot(A,col.regions= terrain.colors(100)). image(A,col=terrain.colors(100)). The parameter 100 specifies the length of the colormap. Other colormaps are heat.colors(), topo.colors(), and cm.colors(). D. Hiebeler, Matlab / R Reference No. 272 Description Build your own colormap using Red/Green/Blue triplets Matlab plotting specifications, Symbol Color Symbol b blue . g green o r red x c cyan + m magenta * y yellow s k black d w white v ^ < > p h Matlab Use an n × 3 matrix; each row gives R,G,B intensities between 0 and 1. Can use as argument with colormap. E.g. for 2 colors: mycmap = [0.5 0.8 0.2 ; 0.2 0.2 0.7] 32 R Use a vector of hexadecimal strings, each beginning with ’#’ and giving R,G,B intensities between 00 and FF. E.g. c(’#80CC33’,’#3333B3’); can use as argument to col= parameter to image. You can build such a vector of strings from vectors of Red, Green, and Blue intensities (each between 0 and 1) as follows (for a 2-color example): r=c(0.5,0.2); g=c(0.8,0.2); b=c(0.2,0.7); mycolors=rgb(r,g,b). for use with plot, fplot, semilogx, semilogy, loglog, etc: Marker Symbol Linestyle point (.) solid line circle (◦) : dotted line cross (×) -. dash-dot line plus sign (+) -dashed line asterisk (∗) square (¤) diamond (♦) triangle (down) (▽) triangle (up) (△) triangle (left) (⊳) triangle (right) (⊲) pentragram star hexagram star R plotting specifications for col (color), pch (plotting character), and type arguments, for use with plot, matplot, points, and lines: col Description pch Description type Description ’blue’ Blue ’a’ a (similarly for other p points characters, but see ’.’ below for an exception ’green’ Green 0 open square l lines ’red’ Red 1 open circle b both ’cyan’ Cyan 2 triangle point-up c lines part only of “b” ’magenta’ Magenta 3 + (plus) o lines, points overplotted ’yellow’ Yellow 4 × (cross) h histogram-like lines ’black’ Black 5 diamond s steps ’#RRGGBB’ hexadecimal specifica6 triangle point-down S another kind of steps tion of Red, Green, Blue (Other names) See colors() for list of ’.’ rectangle of size 0.01 n no plotting (can be useavailable color names. inch, 1 pixel, or 1 point ful for setting up axis (1/72 inch) depending ranges, etc.) on device (See table on next page for more) D. Hiebeler, Matlab / R Reference 33 R plotting specifications for lty (line-type) argument, for use with plot, matplot, points, and lines: lty Description 0 blank 1 solid 2 dashed 3 dotted 4 dotdash 5 longdash 6 twodash # # 24 25 A A b b 18 19 20 21 22 23 12 13 14 15 16 17 6 7 8 9 10 11 0 1 2 3 4 5 . R plotting characters, i.e. values for pch argument (from the book R Graphics, by Paul Murrell, Chapman & Hall / CRC, 2006) D. Hiebeler, Matlab / R Reference No. 273 Description Divide up a figure window into smaller sub-figures Matlab subplot(m,n,k) divides the current figure window into an m × n array of subplots, and draws in subplot number k as numbered in “reading order,” i.e. left-to-right, top-tobottom. E.g. subplot(2,3,4) selects the first sub-figure in the second row of a 2 × 3 array of sub-figures. You can do more complex things, e.g. subplot(5,5,[1 2 6 7]) selects the first two subplots in the first row, and first two subplots in the second row, i.e. gives you a bigger subplot within a 5 × 5 array of subplots. (If you that command followed by e.g. subplot(5,5,3) you’ll see what’s meant by that.) 274 Force graphics windows to update drawnow (Matlab normally only updates figure windows when a script/function finishes and returns control to the Matlab prompt, or under a couple of other circumstances. This forces it to update figure windows to reflect any recent plotting commands.) 34 R There are several ways to do this, e.g. using layout or split.screen, although they aren’t quite as friendly as Matlab’s. E.g. if you let A = 1 1 2 1 1 3 , then layout(A) will 4 5 6 divide the figure into 6 sub-figures: you can imagine the figure divide into a 3 × 3 matrix of smaller blocks; subfigure 1 will take up the upper-left 2 × 2 portion, and sub-figures 2–6 will take up smaller portions, according to the positions of those numbers in the matrix A. Consecutive plotting commands will draw into successive subfigures; there doesn’t seem to be a way to explicitly specify which sub-figure to draw into next. To use split.screen, you can do e.g. split.screen(c(2,1)) to split into a 2 × 1 matrix of subfigures (numbered 1 and 2). Then split.screen(c(1,3),2) splits subfigure 2 into a 1 × 3 matrix of smaller sub-figures (numbered 3, 4, and 5). screen(4) will then select sub-figure number 4, and subsequent plotting commands will draw into it. A third way to accomplish this is via the commands par(mfrow=) or par(mfcol=) to split the figure window, and par(mfg=) to select which sub-figure to draw into. Note that the above methods are all incompatible with each other. R automatically updates graphics windows even before functions/scripts finish executing, so it’s not necessary to explictly request it. But note that some graphics functions (particularly those in the lattice package) don’t display their results when called from scripts or functions; e.g. rather than levelplot(...) you need to do print(levelplot(...)). Such functions will automatically display their plots when called interactively from the command prompt. D. Hiebeler, Matlab / R Reference 7.2 35 Printing/saving graphics No. 275 Description To print/save to a PDF file named fname.pdf Matlab print -dpdf fname saves the contents of currently active figure window 276 To print/save to a PostScript file fname.ps or fname.eps print -dps fname for black & white PostScript; print -dpsc fname for color PostScript; print -deps fname for black & white Encapsulated PostScript; print -depsc fname for color Encapsulated PostScript. The first two save to fname.ps, while the latter two save to fname.eps. 277 To print/save to a JPEG file fname.jpg with jpeg quality = 90 (higher quality looks better but makes the file larger) print -djpeg90 fname R First do pdf(’fname.pdf’). Then, do various plotting commands to make your image, as if you were plotting in a window. Finally, do dev.off() to close/save the PDF file. To print the contents of the active figure window, do dev.copy(device=pdf, file=’fname.pdf’); dev.off(). (But this will not work if you’ve turned off the display list via dev.control(displaylist= ’inhibit’).) You can also simply use dev.copy2pdf(file=’fname.pdf’). postscript(’fname.eps’), followed by your plotting commands, followed by dev.off() to close/save the file. Note: you may want to use postscript(’fname.eps’, horizontal=FALSE) to save your figure in portrait mode rather than the default landscape mode. To print the contents of the active figure window, do dev.copy(device=postscript, file=’fname.eps’); dev.off(). (But this will not work if you’ve turned off the display list via dev.control(displaylist= ’inhibit’).) You can also include the horizontal=FALSE argument with dev.copy(). The command dev.copy2eps(file=’fname.eps’) also saves in portrait mode. jpeg(’fname.jpg’,quality=90), followed by your plotting commands, followed by dev.off() to close/save the file. D. Hiebeler, Matlab / R Reference 7.3 No. 278 36 Animating cellular automata / lattice simulations Description To display images of cellular automata or other lattice simulations while running in real time Matlab Repeatedly use either pcolor or image to display the data. Don’t forget to call drawnow as well, otherwise the figure window will not be updated with each image. R If you simply call image repeatedly, there is a great deal of flickering/flashing. To avoid this, after drawing the image for the first time using e.g. image(A), from then on only use image(A,add=TRUE), which avoids redrawing the entire image (and the associated flicker). However, this will soon consume a great deal of memory, as all drawn images are saved in the image buffer. There are two solutions to that problem: (1) every k time steps, leave off the “add=TRUE” argument to flush the image buffer (and get occasional flickering), where you choose k to balance the flickering vs. memory-usage tradeoff; or (2) after drawing the first image, do dev.control(displaylist= ’inhibit’) to prohibit retaining the data. However, the latter solution means that after the simulation is done, the figure window will not be redrawn if it is resized, or temporarily obscured by another window. (A call to dev.control(displaylist= ’enable’) and then one final image(A) at the end of the simulation will re-enable re-drawing after resizing or obscuring, without consuming extra memory.) D. Hiebeler, Matlab / R Reference 8 No. 279 280 281 282 283 284 285 37 Working with files Description Create a folder (also known as a “directory”) Set/change working directory See list of files in current working directory Run commands in file ‘foo.m’ or ‘foo.R’ respectively Read data from text file “data.txt” into matrix A Read data from text file “data.txt” into matrix A, skipping the first s lines of the file Write data from matrix A into text file “data.txt” Matlab mkdir dirname R dir.create(’dirname’) cd dirname dir setwd(’dirname’) dir() foo source(’foo.R’) A=load(’data.txt’) or A=importdata(’data.txt’) Note that both routines will ignore comments (anything on a line following a “%” character) A=as.matrix(read.table( ’data.txt’)) This will ignore comments (anything on a line following a “#” character). To ignore comments indicated by “%”, do A=as.matrix(read.table( ’data.txt’, comment.char=’%’)) A=as.matrix(read.table( ’data.txt’, skip=s)) tmp=importdata(’data.txt’, ’ ’,s); a=tmp.data save data.txt A -ascii write(t(A), file=’data.txt’, ncolumn=dim(A)[2]) D. Hiebeler, Matlab / R Reference 9 38 Miscellaneous 9.1 Variables No. 286 Description Assigning to variables Matlab x = 5 287 From within a function, assign a value to variable y in the base environment (i.e. the command prompt environment) From within a function, access the value of variable y in the base environment (i.e. the command prompt environment) assignin(’base’, ’y’, 7) who whos whos ab whos *ab* ls.str(pattern=’ab’) openvar(A), or double-click on the variable in the Workspace pane (if it’s being displayed) of your Matlabdesktop fix(A) 294 295 296 297 Short list of defined variables Long list of defined variables See detailed info about the variable ab See detailed info about all variables with “ab” in their name Open graphical data editor, to edit the value of variable A (useful for editing values in a matrix, though it works for non-matrix variables as well) Clear one variable Clear two variables Clear all variables See what type of object x is get(’y’, envir=globalenv()) Though note that inside a function, if there isn’t a local variable y, then just the expression y will look for one in the base environment, but if there is a local y then that one will be used instead. ls() ls.str() str(ab) clear x clear x y clear all class(x) 298 (Variable names) Variable names must begin with a letter, but after that they may contain any combination of letters, digits, and the underscore character. Names are case-sensitive. 299 Result of last command ans contains the result of the last command which did not assign its value to a variable. E.g. after 2+5; x=3, then ans will contain 7. rm(x) rm(x,y) rm(list=ls()) class(x) and typeof(x) give different aspects of the “type” of x Variable names may contain letters, digits, the period, and the underscore character. They cannot begin with a digit or underscore, or with a period followed by a digit. Names are casesensitive. .Last.value contains the result of the last command, whether or not its value was assigned to a variable. E.g. after 2+5; x=3, then .Last.value will contain 3. 288 289 290 291 292 293 evalin(’base’, ’y’) R x <- 5 or x = 5 Note: for compatibility with S-plus, many people prefer the first form. y <<- 7 D. Hiebeler, Matlab / R Reference 9.2 39 Strings and Misc. No. 300 Description Line continuation 301 Controlling output formatting Matlab If you want to break up a Matlab command over more than one line, end all but the last line with three periods: “...”. E.g.: x = 3 + ... 4 or x = 3 ... + 4 of format short g format long g are help format handy; and see 302 303 304 Exit the program Comments Display a string quit or exit % this is a comment disp(’hi there’) or omit trailing newline fprintf(’hi there’) 305 Display a string containing single quotes 306 Give prompt and read numerical input from user disp(’It’’s nice’) or to omit trailing newline fprintf(’It’’s nice’) x = input(’Enter data:’) 307 Give prompt and read character (string) input from user Concatenate strings Concatenate strings stored in a vector 308 309 310 Extract substring of a string 311 Determine whether elements of a vector are in a set, and give positions of corresponding elements in the set. to use x = input(’Enter string:’,’s’) [’two hal’ ’ves’] v={’two ’, ’halves’}; strcat(v{:}) But note that this drops trailing spaces on strings. To avoid that, instead do strcat([v{:}]) text1=’hi there’; text2=text(2:6) x = {’a’, ’aa’, ’bc’, ’c’}; y = {’da’, ’a’, ’bc’, ’a’, ’bc’, ’aa’}; [tf, loc]=ismember(x,y) Then loc contains the locations of last occurrences of elements of x in the set y, and 0 for unmatched elements. R In R, you can spread commands out over multiple lines, and nothing extra is necessary. R will continue reading input until the command is complete. However, this only works when the syntax makes it clear that the first line was not complete. E.g.: x = 3 + 4 works, but x = 3 + 4 does not treat the second line as a continuation of the first. options(digits=6) tells R you’d like to use 6 digits of precision in values it displays (it is only a suggestion, not strictly followed) q() or quit() # this is a comment print(’hi there’) Note: to avoid having double-quotes around the displayed string, do print(’hi there’, quote=FALSE) or print(noquote(’hi there’)). print(’It\’s nice’) or print("It’s nice") print(’Enter data:’); x=scan() But note: if in a script and you use the Edit → Execute menu item to run it, the selected text after the scan statement will be used as source for the input, rather than keyboard. x = readline(’Enter string:’) paste(’two hal’, ’ves’, sep=’’) v=c(’two ’, ’halves’); paste(v, collapse=’’) text1=’hi there’; text2=substr(text1,2,6) x = c(’a’, ’aa’, ’bc’, ’c’); y = c(’da’, ’a’, ’bc’, ’a’, ’bc’, ’aa’); loc=match(x,y) Then loc contains the locations of first occurences of elements of x in the set y, and NA for unmatched elements. D. Hiebeler, Matlab / R Reference No. 312 Description Find indices of regular expression pattern p in string s 313 Perform some commands only if the regular expression p is contained in the string s 314 315 316 317 318 319 320 321 322 323 324 40 Matlab v=regexp(s,p) R v=gregexpr(p,s)[[1]] (The returned vector also has a “match.length” attribute giving lengths of the matches; this attribute can be removed via attributes(v)=NULL.) if (regexp(s,p) ...commands... end if (grepl(p,s)) { ...commands... } Convert number to string Use sprintf to create a formatted string. Use %d for integers (“d” stands for “decimal”, i.e. base 10), %f for floating-point numbers, %e for scientific-notation floating point, %g to automatically choose %e or %f based on the value. You can specify field-widths/precisions, e.g. %5d for integers with padding to 5 spaces, or %.7f for floating-point with 7 digits of precision. There are many other options too; see the docs. Machine epsilon ǫmach , i.e. difference between 1 and the next largest double-precision floating-point number Pause for x seconds Wait for user to press any key num2str(x) as.character(x) x=2; y=3.5; s=sprintf(’x is %d, y=%g’, ... x, y) x=2; y=3.5 s=sprintf(’x is %d, y is %g’, x, y) eps (See help eps for various other things eps can give.) .Machine$double.eps pause(x) pause Produce a beep (or possibly a visual signal, depending on preferences set) Measure CPU time used to do some commands Measure elapsed (“wallclock”) time used to do some commands Print an error message an interrupt execution Print a warning message Putting multiple statements on one line beep Sys.sleep(x) Don’t know of a way to do this in R, but scan(quiet=TRUE) will wait until the user presses the Enter key alarm() t1=cputime; ...commands... ; cputime-t1 tic; ...commands... ; toc or t1=clock; ...commands... ; etime(clock,t1) error(’Problem!’) t1=proc.time(); ...commands... ; (proc.time()-t1)[1] t1=proc.time(); ...commands... ; (proc.time()-t1)[3] warning(’Smaller problem!’) Separate statements by commas or semicolons. A semicolon at the end of a statement suppresses display of the results (also useful even with just a single statement on a line), while a comma does not. warning(’Smaller problem!’) Separate statements by semicolons. stop(’Problem!’) D. Hiebeler, Matlab / R Reference No. 325 326 Description Evaluate contents of a string s as command(s). Get a command prompt for debugging, while executing a script or function. While at that prompt, you can type expressions to see the values of variables, etc. 327 Show where a command is 328 Query/set the search path. 41 Matlab eval(s) R eval(parse(text=s)) Insert the command keyboard in your file. Note that your prompt will change to K>>. When you are done debugging and want to continue executing the file, type return. Insert the command browser() in your file. Note that your prompt will change to Browse[1]>. When you are done debugging and want to continue executing the file, either type c or just press return (i.e. enter a blank line). Note, if you type n, you enter the step debugger. R does not execute commands directly from files, so there is no equivalent command. which sqrt shows you where the file defining the sqrt function is (but note that many basic functions are “built in,” so the Matlab function file is really just a stub containing documentation). This is useful if a command is doing something strange, e.g. sqrt isn’t working. If you’ve accidentally defined a variable called sqrt, then which sqrt will tell you, so you can clear sqrt to erase it so that you can go back to using the function sqrt. path displays the current search path (the list of places Matlab searches for commands you enter). To add a directory ~/foo to the beginning of the search path, do R does not use a search path to look for files. addpath ~/foo -begin 329 Startup sequence 330 Shutdown sequence or to add it to the end of the path, do addpath ~/foo -end (Note: you should generally add the full path of a directory, i.e. in Linux or Mac OS-X something like ~/foo as above or of the form /usr/local/lib/foo, while under Windows it would be something like C:/foo) If a file startup.m exists in the startup directory for Matlab, its contents are executed. (See the Matlab docs for how to change the startup directory.) Upon typing quit or exit, Matlab will run the script finish.m if present somewhere in the search path. If a file .Rprofile exists in the current directory or the user’s home directory (in that order), its contents are sourced; saved data from the file .RData (if it exists) are then loaded. If a function .First() has been defined, it is then called (so the obvious place to define this function is in your .Rprofile file). Upon typing q() or quit(), R will call the function .Last() if it has been defined (one obvious place to define it would be in the .Rprofile file) D. Hiebeler, Matlab / R Reference No. 331 Description Install and load a package. 10 No. 332 333 334 335 Matlab Matlab does not have packages. It has toolboxes, which you can purchase and install. “Contributed” code (written by end users) can simply be downloaded and put in a directory which you then add to Matlab’s path (see item 328 for how to add things to Matlab’s path). 42 R To install e.g. the deSolve package, you can use the command install.packages(’deSolve’). You then need to load the package in order to use it, via the command library(’deSolve’). When running R again later you’ll need to load the package again to use it, but you should not need to re-install it. Note that the lattice package is typically included with binary distributions of R, so it only needs to be loaded, not installed. Spatial Modeling Description Take an L×L matrix A of 0s and 1s, and “seed” fraction p of the 0s (turn them into 1s), not changing entries which are already 1. Take an L × L matrix A of 0s and 1s, and “kill” fraction p of the 1s (turn them into 0s), not changing the rest of the entries Do “wraparound” on a coordinate newx that you’ve already calculated. You can replace newx with x+dx if you want to do wraparound on an offset x coordinate. Randomly initialize a portion of an array: set fraction p of sites in rows iy1 through iy2 and columns ix1 through ix2 equal to 1 (and set the rest of the sites in that block equal to zero). Note: this assume iy1 < iy2 and ix1 < ix2. Matlab A = (A | (rand(L) < p))*1; R A = (A | (matrix(runif(L^2),L) < p))*1 A = (A & (rand(L) < 1-p))*1; A = (A & (matrix(runif(L^2),L) < 1-p))*1 mod(newx-1,L)+1 Note: for portability with other languages such as C which handle MOD of negative values differently, you may want to get in the habit of instead doing mod(newx-1+L,L)+1 dx=ix2-ix1+1; dy=iy2-iy1+1; A(iy1:iy2,ix1:ix2) = ... (rand(dy,dx) < p0)*1; ((newx-1) %% L) + 1 Note: for portability with other languages such as C which handle MOD of negative values differently, you may want to get in the habit of instead doing ((newx-1+L)%%L) + 1 dx=ix2-ix1+1; dy=iy2-iy1+1; A[iy1:iy2,ix1:ix2] = (matrix(runif(dy*dx),dy) < p0)*1 INDEX OF MATLAB COMMANDS AND CONCEPTS 43 Index of MATLAB commands and concepts ’, 83 ,, 324 .*, 82 ..., 300 ./, 90 .^, 94 /, 89 :, 12–14 ;, 324 =, 286 [, 6–8 %, 303 &, 186, 187 ^, 54, 92, 93 \, 84, 91 { 49 abs, 55, 74 acos, 60 acosh, 62 addpath, 328 all, 188 angle, 75 annotation, 263, 264 ans, 299 any, 189 arrows in plots, 263, 264 asin, 60 asinh, 62 assignin, 287 atan, 60 atanh, 62 average, see mean axis, 255 bar, 244, 246, 247 beep, 319 binocdf, 229 binopdf, 222 binornd, 213 boolean tests scalar, 186 vector, 187–189 break, 191 cd, 280 ceil, 66 cell, 48 cell arrays, 48 extracting elements of, 49 cellular automata animation, 278 chol, 100 circshift, 33 class, 297 clear, 294–296 clf, 266 clock, 321 close, 239 colon, see : colorbar, 270 colormap building your own, 272 colormap, 271, 272 column vector, 7 comments, 303 complex numbers, 73–78 cond, 104–106 conj, 76 continue, 191 contour, 254 conv, 165 corr, 118–123 cos, 59 cosh, 61 cov, 116, 117 cputime, 320 cross, 80 csape, 178, 180, 181 cubic splines, 179, 180 natural, 178 not-a-knot, 182 periodic, 181 cumprod, 135 cumsum, 131–134 cumulative distribution functions binomial, 229 continuous uniform on interval (a, b), 233 discrete uniform from 1..n, 234 exponential, 231 normal, 232 Poisson, 230 debugging, 326 det, 86 diag, 22, 23 diff, 137 differential equations, see ode45 dir, 281 disp, 304, 305 doc, 4 dot, 79 INDEX OF MATLAB COMMANDS AND CONCEPTS drawnow, 274, 278 echelon form, see matrix eig, 96 element-by-element matrix operations, see matrix else, 185 elseif, 185 end, 40 eps, 316 erf, 68 erfc, 69 erfcinv, 71 erfinv, 70 error, 322 errorbar, 248, 249 etime, 321 eval, 325 evalin, 288 exit, 302, 330 exp, 56 expcdf, 231 expm, 130 exppdf, 224 exprnd, 215 eye, 21 figure, 235, 236 file running commands in, 282 text reading data from, 283, 284 saving data to, 285 find, 160–162 finish.m, 330 fliplr, 34 flipud, 35 floor, 65 fminbnd, 168, 169 fminsearch, 170, 171 font size in plots, 259 for, 183 format, 301 fplot, 268 fprintf, 304, 305 function multi-variable minimization, 170 minimization over first parameter only, 169 minimization over only some parameters, 171 single-variable minimization, 168 user-written, 193 returning multiple values, 194 fzero, 167 gca, 259 gcf, 237 get, 238 Greek letters in plot labels, 258 grid, 260 help, 1–3 helpbrowser, 4 helpdesk, 4 hilb, 46 hist, 163, 164, 245, 246 hold, 266 identity, see matrix if, 184–186 imag, 78 image, 269, 278 imagesc, 269 importdata, 283, 284 ind2sub, 36 indexing matrix, 10 with a single index, 11 vector, 9 input, 306, 307 inv, 87 inverse, see matrix ismember, 311 keyboard, 326 legend, 265 length, 150, 152 linspace, 15 load, 283 log, 57 log10, 58 log2, 58 loglog, 243 logspace, 16 lookfor, 5 lu, 97 matrix, 8 boolean operations on, 161, 162 changing shape of, 43 Cholesky factorization, 100 circular shift, 33 condition number, 104–106 44 INDEX OF MATLAB COMMANDS AND CONCEPTS containing all indentical entries, 20 containing all zeros, 19 converting row, column to single index, 37 converting single-index to row, column, 36 cumulative sums of all elements of, 134 cumulative sums of columns, 132 cumulative sums of rows, 133 determinant, 86 diagonal, 22 echelon form, 85 eigenvalues and eigenvectors of, 96 equation solving, 84 exponential of, 130 extracting a column of, 28 extracting a rectangular piece of, 31 extracting a row of, 29 extracting specified rows and columns of, 32 “gluing” together, 24, 25 identity, 21 inverse, 87 lower-triangular portion of, 44 LU factorization, 97 minimum of values of, 140 minimum value of each column of, 141 minimum value of each row of, 142 modifying elements given lists of rows and columns, 38 multiplication, 81 element-by-element, 82 N -dimensional, 47 norm, 103 powers of, 93 product of all elements, 127 of columns of, 128 of rows of, 129 QR factorization, 101 rank, 95 re-shaping its elements into a vector, 30 reverse elements in columns, 35 reverse elements in rows, 34 Schur decomposition, 99 singular value decomposition, 98 size of, 147–149, 151, 152 sum of all elements, 124 of columns of, 125 of rows of, 126 trace, 88 transpose, 83 upper-triangular portion of, 45 max, see min 45 mean, 107–109 mesh, 254 meshgrid, 26, 118, 253 min, 139–142, 144–146 mind, 143 mkdir, 279 mnpdf, 228 mnrnd, 220, 221 mod, 63, 334 modulo arithmetic, 63, 334 multiple statements on one line, 324 nchoosek, 72 norm, 102, 103 normcdf, 232 normpdf, 225 normrnd, 219 num2str, 314 numel, 151 ode45, 195–197 ones, 18, 20 openvar, 293 optimization, 168–171 path, 328 pause, 317, 318 pcolor, 254, 269, 278 perform some commands with probability p, 207 permutation of integers 1..n, 208 plot, 240–242, 267 Greek letters in axis labels, 258 plot3, 251 poisscdf, 230 poisspdf, 223 poissrnd, 214 polar, 250 polyfit, 174–176 polynomial least-squares fitted, 175–177 multiplication, 165 roots of, 166 ppval, 178, 180, 181 print, 275–277 probability density functions binomial, 222 continuous uniform on interval (a, b), 226 discrete uniform from 1..n, 227 exponential, 224 multinomial, 228 normal, 225 Poisson, 223 prod, 127–129 INDEX OF MATLAB COMMANDS AND CONCEPTS qr, 101 quad, 172 quit, 302, 330 rand, 198–206, 212 random values Bernoulli, 204 binomial, 213 continuous uniform distribution on interval (a, b), 201, 218 continuous uniform distribution on interval (0,1), 198–200 discrete uniform distribution from a..b, 206 discrete uniform distribution from 1..k, 203, 216, 217 discrete uniform distribution, 202 exponential, 215 k unique values sampled from integers 1..n, 209 multinomial, 220, 221 normal, 219 Poisson, 214 setting the seed, 212 randperm, 208, 209 randsample, 209–211 rank, 95 rcond, 104 real, 77 regexp, 312, 313 reshape, 43, 47 roots of general single-variable function, 167 polynomial, 166 roots, 166 round, 64 row vector, 6 rref, 85 sampling values from a vector, 210, 211 save, 285 schur, 99 semilogx, 243 semilogy, 243 set, 259 shading, 269 sign, 67 sin, 59 sinh, 61 size, 147–149 slice, 254 sort, 153, 154, 209 sortrows, 155–158 spline, 182 46 splines, see cubic splines sprintf, 315 sqrt, 53 stairs, 250 standard deviation, see std startup.m, 329 std, 110–112 stem, 250 stop, 322 strcat, 309 string concatenation, 308 converting number to, 314 pattern matching, 312, 313 substrings, 310 struct, 51 sub2ind, 37, 38 subplot, 273 sum, 124–126, 187 surf, 252, 253 surfc, 254 surfl, 254 svd, 98 switch, 192 tan, 59 tanh, 61 text, 261, 262 tic, 321 title, 256 toc, 321 trace, 88 transpose, see matrix trapz, 173 tril, 44 triu, 45 unidcdf, 234 unidpdf, 227 unidrnd, 216, 217 unifcdf, 233 unifpdf, 226 unifrnd, 218 unique, 163, 246 var, 113–115 variables assigning, 286 assigning in base environment from function, 287 evaluating from base environment within function, 288 names, 298 variance, see var INDEX OF MATLAB COMMANDS AND CONCEPTS vector boolean operations on, 159, 160 containing all indentical entries, 18 containing all zeros, 17 counts of binned values in, 164 counts of discrete values in, 163 cross product, 80 cumulative sum of elements of, 131 differences between consecutive elements of, 137 dot product, 79 minimum of values of, 139 norm, 102 position of first occurance of minimum value in, 146 product of all elements, 127 reversing order of elements in, 27 size of, 150 sum of all elements, 124 truncating, 39 warning, 323 waterfall, 254 which, 327 while, 190 who, 289 whos, 290–292 xlabel, 257–259 ylabel, 257, 258 zeros, 17, 19 47 INDEX OF R COMMANDS AND CONCEPTS 48 Index of R commands and concepts *, 92 /, 90 :, 12, 13 ;, 324 <-, 286 <<-, 287 =, 286 ?, 1, 2 [[, 49 #, 303 %%, 63, 334 &, 186, 187 ^, 54, 94 abs, 55, 74 acos, 60 acosh, 62 alarm, 319 all, 188 any, 189 apply, 34, 35, 112, 114, 115, 128, 141, 142 Arg, 75 array, 47 arrows, 263, 264 as.character, 314 as.formula, 176 as.numeric, 163 asin, 60 asinh, 62 atan, 60 atanh, 62 average, see mean barplot, 244, 246 boolean tests scalar, 186 vector, 187–189 break, 191 browser, 326 c, 6, 7 cbind, 24, 38 ceiling, 66 cellular automata animation, 278 chol, 100 choose, 72 class, 297 cloud, 251 coef, 174–177 colMeans, 108 colon, see : colormap building your own, 272 for image, 271 colSums, 125 column vector, 7 comments, 303 complex numbers, 73–78 Conj, 76 contour, 254 convolve, 165 cor, 119–123 cos, 59 cosh, 61 cov, 116–118 cubic splines, 179, 180, 182 natural, 178 periodic, 181 cummax, 136 cummin, 136 cumprod, 135 cumsum, 131–134 cumulative distribution functions binomial, 229 continuous uniform on interval (a, b), 233 discrete uniform from 1..n, 234 exponential, 231 normal, 232 Poisson, 230 curve, 268 data.frame, 51 dbinom, 222 debugging, 326 det, 86 dev.control, 275, 276, 278 dev.copy, 275, 276 dev.copy2eps, 276 dev.copy2pdf, 275 dev.cur(), 237 dev.list, 238 dev.new, 235 dev.off, 239, 275–277 dev.set, 236 dexp, 224 diag, 21–23 diff, 137 differential equations, see lsoda dim, 43, 149, 152 dir, 281 dir.create, 279 INDEX OF R COMMANDS AND CONCEPTS dmultinom, 228 dnorm, 225 dpois, 223 dunif, 226 echelon form, see matrix eig, 96 element-by-element matrix operations, see matrix else, 185 errbar, 248, 249 eval, 325 exp, 56 expand, 97 expand.grid, 254 expm, 130 file running commands in, 282 text reading data from, 283, 284 saving data to, 285 filled.contour, 270 .First, 329 fix, 293 floor, 65 font size in plots, 259 for, 183 function multi-variable minimization, 170 minimization over first parameter only, 169 minimization over only some parameters, 171 single-variable minimization, 168 user-written, 193 returning multiple values, 194 get, 288 globalenv, 288 graphics not being displayed from scripts/functions, 274 Greek letters in plot labels, 258 gregexpr, 312 grepl, 313 grid, 260 help, 1, 2 help.search, 5 help.start, 4 Hilbert, 46 49 hist, 164, 244, 245, 247 identity, see matrix if, 184–186 ifelse, 138 Im, 78 image, 269, 278 indexing matrix, 10 with a single index, 11 vector, 9 install.packages, 331 integrate, 172 inverse, see matrix jpeg, 277 kappa, 105 .Last, 330 .Last.value, 299 lattice package, 254, 270, 274, 331 layout, 273 legend, 265 length, 39, 40, 150, 151 levelplot, 270, 274 library, 3, 331 lines, 266 lists, 48 extracting elements of, 49 lm, 174–177 lm.fit, 176 log, 57 log10, 58 log2, 58 lower.tri, 45 ls, 289 ls.str, 290, 292 lsoda, 195–197 .Machine$double.eps, 316 match, 311 matplot, 267 matrix, 8 boolean operations on, 161, 162 changing shape of, 43 Cholesky factorization, 100 circular shift, 33 condition number, 104–106 containing all indentical entries, 20 containing all zeros, 19 converting row, column to single index, 37 converting single-index to row, column, 36 cumulative sums of all elements of, 134 INDEX OF R COMMANDS AND CONCEPTS cumulative sums of columns, 132 cumulative sums of rows, 133 determinant, 86 diagonal, 22 echelon form, 85 eigenvalues and eigenvectors of, 96 equation solving, 84 exponential of, 130 extracting a column of, 28 extracting a rectangular piece of, 31 extracting a row of, 29 extracting specified rows and columns of, 32 “gluing” together, 24, 25 identity, 21 inverse, 87 lower-triangular portion of, 44 LU factorization, 97 minimum of values of, 140 minimum value of each column of, 141 minimum value of each row of, 142 modifying elements given lists of rows and columns, 38 multiplication, 81 element-by-element, 82 N -dimensional, 47 norm, 103 powers of, 93 product of all elements, 127 of columns of, 128 of rows of, 129 QR factorization, 101 rank, 95 re-shaping its elements into a vector, 30 reverse elements in columns, 35 reverse elements in rows, 34 Schur decomposition, 99 singular value decomposition, 98 size of, 147–149, 151, 152 sum of all elements, 124 of columns of, 125 of rows of, 126 trace, 88 transpose, 83 upper-triangular portion of, 45 matrix, 8, 19, 20 max, see min mean, 107 min, 139–142, 145 Mod, 74 modulo arithmetic, 63, 334 50 multiple statements on one line, 324 names, 50, 163 ncol, 148 next, 191 norm, 102, 103 nrow, 147 optim, 170, 171 optimization, 168–171 optimize, 168, 169 options digits=, 301 order, 155–158 outer, 176, 253 packages installing, 331 loading, 331 par, 259 par mfcol=, 273 mfrow=, 273 parse, 325 paste, 176, 308, 309 pbinom, 229 pdf, 259, 275 perform some commands with probability p, 207 permutation of integers 1..n, 208 persp, 252, 253 pexp, 231 pie, 250 plot, 240–243 Greek letters in axis labels, 258 main=, 256 sub=, 256 xlab=, 257, 258 xlim=, 255 ylab=, 257, 258 ylim=, 255 pmin, 143, 144 pnorm, 68, 69, 232 points, 266 polynomial least-squares fitted, 175–177 multiplication, 165 roots of, 166 polyreg, 176 polyroot, 166 postscript, 276 ppois, 230 print, 274, 304, 305 probability density functions binomial, 222 INDEX OF R COMMANDS AND CONCEPTS continuous uniform on interval (a, b), 226 discrete uniform from 1..n, 227 exponential, 224 multinomial, 228 normal, 225 Poisson, 223 proc.time, 320, 321 prod, 127–129 punif, 233 q, 302, 330 qnorm, 70, 71 qr, 95, 101 quartz, 235 quit, 302, 330 rand, 205 random values Bernoulli, 204 binomial, 213 continuous uniform distribution on interval (a, b), 201, 218 continuous uniform distribution on interval (0,1), 198, 200 continuous uniform distribution on inteval (0,1), 199 discrete uniform distribution from a..b, 206 discrete uniform distribution from 1..k, 203, 216, 217 discrete uniform distribution, 202 exponential, 215 k unique values sampled from integers 1..n, 209 multinomial, 220, 221 normal, 219 Poisson, 214 setting the seed, 212 rbind, 25 rbinom, 213 rcond, 104, 106 .RData, 329 Re, 77 read.table, 283, 284 readline, 307 rep, 17, 18 rev, 27 rexp, 215 rgb, 272 rm, 294–296 rmultinom, 220, 221 rnorm, 219 roots of general single-variable function, 167 51 polynomial, 166 round, 64 row vector, 6 rowMeans, 109 rpois, 214 .Rprofile, 329 runif, 198–204, 206, 218 sample, 208–211, 216, 217 sampling values from a vector, 210, 211 scan, 306, 318 Schur, 99 sd, 110–112 seq, 14–16 set.seed, 212 setwd, 280 sign, 67 sin, 59 sinh, 61 solve, 84, 87, 89, 91 sort, 153, 154 source, 282 spline, 178, 179, 181 splines, see cubic splines split.screen, 273 sprintf, 315 sqrt, 53 standard deviation, see sd str, 291 string concatenation, 308 converting number to, 314 pattern matching, 312, 313 substrings, 310 substr, 310 sum, 124, 126, 187 svd, 98 switch, 192 symbols, 254 Sys.sleep, 317 t, 83 table, 163, 246 tan, 59 tanh, 61 text, 261, 262 title, 256, 257 transpose, see matrix typeof, 297 uniroot, 167 upper.tri, 44 var, 113–115, 117 INDEX OF R COMMANDS AND CONCEPTS variables assigning, 286 assigning in base environment from function, 287 evaluating from base environment within function, 288 names, 298 variance, see var vector boolean operations on, 159, 160 containing all indentical entries, 18 containing all zeros, 17 counts of binned values in, 164 counts of discrete values in, 163 cross product, 80 cumulative sum of elements of, 131 differences between consecutive elements of, 137 dot product, 79 minimum of values of, 139 norm, 102 position of first occurance of minimum value in, 146 product of all elements, 127 reversing order of elements in, 27 size of, 150 sum of all elements, 124 truncating, 39 vector, 48 warning, 323 which, 160–162 which.max, see which.min which.min, 146 while, 190 windows, 235 wireframe, 254 write, 285 x11, 235 52

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