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					MATLAB commands in numerical Python (NumPy) Vidar Bronken Gundersen /mathesaurus.sf.net

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MATLAB commands in numerical Python (NumPy)
Copyright c  Vidar Bronken Gundersen Permission is granted to copy, distribute and/or modify this document as long as the above attribution is kept and the resulting work is distributed under a license identical to this one. The idea of this document (and the corresponding xml instance) is to provide a quick reference for switching from matlab to an open-source environment, such as Python, Scilab, Octave and Gnuplot, or R for numeric processing and data visualisation. Where Octave and Scilab commands are omitted, expect Matlab compatibility, and similarly where non given use the generic command. Time-stamp: --T:: vidar

1

Help
matlab/Octave doc Octave: help -i % browse with Info help help or doc doc help plot help splines or doc splines demo Python help() help help(plot) or ?plot help(pylab) R help.start() help() help(plot) or ?plot help(package=’splines’) demo() example(plot)

Desc. Browse help interactively Help on using help Help for a function Help for a toolbox/library package Demonstration examples Example using a function

1.1

Searching available documentation
matlab/Octave lookfor plot help which plot Python R help.search(’plot’) apropos(’plot’) library() find(plot) methods(plot)

Desc. Search help files Find objects by partial name List available packages Locate functions List available methods for a function

help(); modules [Numeric] help(plot)

1.2

Using interactively
matlab/Octave Octave: octave -q Octave: TAB or M-? foo(.m) Octave: history diary on [..] diary off exit or quit Python ipython -pylab TAB execfile(’foo.py’) or run foo.py hist -n CTRL-D CTRL-Z # windows sys.exit() R Rgui source(’foo.R’) history() savehistory(file=".Rhistory") q(save=’no’)

Desc. Start session Auto completion Run code from file Command history Save command history End session

2

Operators
matlab/Octave help Python R help(Syntax)

Desc. Help on operator syntax

 References: Hankin, Robin. R for Octave users (), available from http://cran.r-project.org/doc/contrib/R-and-octave-.txt (accessed ..); Martelli, Alex. Python in a Nutshell (O’Reilly, ); Oliphant, Travis. Guide to NumPy (Trelgol, ); Hunter, John. The Matplotlib User’s Guide (), available from http://matplotlib.sf.net/ (accessed ..); Langtangen, Hans Petter. Python Scripting for Computational Science (Springer, ); Ascher et al.: Numeric Python manual (), available from http://numeric.scipy.org/numpy.pdf (accessed ..); Moler, Cleve. Numerical Computing with MATLAB (MathWorks, ), available from http://www.mathworks.com/moler/ (accessed ..); Eaton, John W. Octave Quick Reference (); Merrit, Ethan. Demo scripts for gnuplot version 4.0 (), available from http://gnuplot.sourceforge.net/demo/ (accessed ..); Woo, Alex. Gnuplot Quick Reference (), available from http://www.gnuplot.info/docs/gpcard.pdf (accessed ..); Venables & Smith: An Introduction to R (), available from http://cran.r-project.org/doc/manuals/R-intro.pdf (accessed ..); Short, Tom. R reference card (), available from http://www.rpad.org/Rpad/R-refcard.pdf (accessed ..).

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2.1

Arithmetic operators
matlab/Octave a=1; b=2; a + b a - b a * b a / b a .^ b Python a=1; b=1 a + b or add(a,b) a - b or subtract(a,b) a * b or multiply(a,b) a / b or divide(a,b) a ** b power(a,b) pow(a,b) a % b remainder(a,b) fmod(a,b) a+=b or add(a,b,a) factorial(a) R a<-1; b<-2 a + b a - b a * b a / b a ^ b

Desc. Assignment; defining a number Addition Subtraction Multiplication Division Power, ab

Remainder

rem(a,b)

a %% b

Integer division In place operation to save array creation overhead Factorial, n!

a %/% b Octave: a+=1 factorial(a)

2.2

Relational operators
matlab/Octave a == b a < b a > b a <= b a >= b a ~= b Python a == b or equal(a,b) a < b or less(a,b) a > b or greater(a,b) a <= b or less_equal(a,b) a >= b or greater_equal(a,b) a != b or not_equal(a,b) R a == b a < b a > b a <= b a >= b a != b

Desc. Equal Less than Greater than Less than or equal Greater than or equal Not Equal

2.3

Logical operators
matlab/Octave a && b a || b a & b or and(a,b) a | b or or(a,b) xor(a, b) ~a or not(a) Octave: ~a or !a any(a) all(a) Python a and b a or b logical_and(a,b) or a and b logical_or(a,b) or a or b logical_xor(a,b) logical_not(a) or not a R a && b a || b a & b a | b xor(a, b) !a

Desc. Short-circuit logical AND Short-circuit logical OR Element-wise logical AND Element-wise logical OR Logical EXCLUSIVE OR Logical NOT True if any element is nonzero True if all elements are nonzero

2.4

root and logarithm
matlab/Octave sqrt(a) log(a) log10(a) log2(a) exp(a) Python math.sqrt(a) math.log(a) math.log10(a) math.log(a, 2) math.exp(a) R sqrt(a) log(a) log10(a) log2(a) exp(a) √ a ln a = loge a log10 a log2 a ea

Desc. Square root Logarithm, base e (natural) Logarithm, base  Logarithm, base  (binary) Exponential function

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2.5

Round off
matlab/Octave round(a) ceil(a) floor(a) fix(a) Python around(a) or math.round(a) ceil(a) floor(a) fix(a) R round(a) ceil(a) floor(a)

Desc. Round Round up Round down Round towards zero

2.6

Mathematical constants
matlab/Octave pi exp(1) Python math.pi math.e or math.exp(1) R pi exp(1)

Desc. π = 3.141592 e = 2.718281

2.6.1

Missing values; IEEE-754 floating point status flags
matlab/Octave NaN Inf Python nan inf plus_inf minus_inf plus_zero minus_zero R

Desc. Not a Number Infinity, ∞ Infinity, +∞ Infinity, −∞ Plus zero, +0 Minus zero, −0

2.7

Complex numbers
matlab/Octave i z = 3+4i abs(z) real(z) imag(z) arg(z) conj(z) Python z = 1j z = 3+4j or z = complex(3,4) abs(3+4j) z.real z.imag z.conj(); z.conjugate() R 1i z <- 3+4i abs(3+4i) or Mod(3+4i) Re(3+4i) Im(3+4i) Arg(3+4i) Conj(3+4i) i= √ −1

Desc. Imaginary unit A complex number, 3 + 4i Absolute value (modulus) Real part Imaginary part Argument Complex conjugate

2.8

Trigonometry
matlab/Octave atan(a,b) Python atan2(b,a) hypot(x,y) R atan2(b,a) x2 + y 2

Desc. Arctangent, arctan(b/a) Hypotenus; Euclidean distance

2.9

Generate random numbers
matlab/Octave rand(1,10) Python random.random((10,)) random.uniform((10,)) random.uniform(2,7,(10,)) random.uniform(0,1,(6,6)) random.standard_normal((10,)) R runif(10)

Desc. Uniform distribution

Uniform: Numbers between  and  Uniform: , array Normal distribution

2+5*rand(1,10) rand(6) randn(1,10)

runif(10, min=2, max=7) matrix(runif(36),6) rnorm(10)

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3

Vectors
matlab/Octave a=[2 3 4 5]; adash=[2 3 4 5]’; Python a=array([2,3,4,5]) array([2,3,4,5])[:,NewAxis] array([2,3,4,5]).reshape(-1,1) r_[1:10,’c’] R a <- c(2,3,4,5) adash <- t(c(2,3,4,5))

Desc. Row vector, 1 × n-matrix Column vector, m × 1-matrix

3.1

Sequences
matlab/Octave 1:10 0:9 1:3:10 10:-1:1 10:-3:1 linspace(1,10,7) reverse(a) a(:) = 3 Python arange(1,11, dtype=Float) range(1,11) arange(10.) arange(1,11,3) arange(10,0,-1) arange(10,0,-3) linspace(1,10,7) a[::-1] or a.fill(3), a[:] = 3 R seq(10) or 1:10 seq(0,length=10) seq(1,10,by=3) seq(10,1) or 10:1 seq(from=10,to=1,by=-3) seq(1,10,length=7) rev(a)

Desc. ,,, ... , .,.,., ... ,. ,,, ,,, ... , ,,, Linearly spaced vector of n= points Reverse Set all values to same scalar value

3.2

Concatenation (vectors)
matlab/Octave [a a] [1:4 a] Python concatenate((a,a)) concatenate((range(1,5),a), axis=1) R c(a,a) c(1:4,a)

Desc. Concatenate two vectors

3.3

Repeating
matlab/Octave [a a] Python concatenate((a,a)) a.repeat(3) or a.repeat(a) or R rep(a,times=2) rep(a,each=3) rep(a,a)

Desc.   ,      ,   ,    ,  ,   

3.4

Miss those elements out
matlab/Octave a(2:end) a([1:9]) a(end) a(end-1:end) Python a[1:] R a[-1] a[-10] a[-seq(1,50,3)]

Desc. miss the first element miss the tenth element miss ,,, ... last element last two elements

a[-1] a[-2:]

3.5

Maximum and minimum
matlab/Octave max(a,b) max([a b]) [v,i] = max(a) Python maximum(a,b) concatenate((a,b)).max() v,i = a.max(0),a.argmax(0) R pmax(a,b) max(a,b) v <- max(a) ; i <- which.max(a)

Desc. pairwise max max of all values in two vectors

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3.6

Vector multiplication
matlab/Octave a.*a dot(u,v) Python a*a dot(u,v) R a*a

Desc. Multiply two vectors Vector dot product, u · v

4

Matrices
matlab/Octave a = [2 3;4 5] Python a = array([[2,3],[4,5]]) R rbind(c(2,3),c(4,5)) array(c(2,3,4,5), dim=c(2,2)) 2 4 3 5

Desc. Define a matrix

4.1

Concatenation (matrices); rbind and cbind
matlab/Octave [a ; b] [a , b] Python R concatenate((a,b), axis=0) rbind(a,b) vstack((a,b)) concatenate((a,b), axis=1) cbind(a,b) hstack((a,b)) concatenate((a,b), axis=2) dstack((a,b)) concatenate((a,b), axis=None) concatenate((r_[1:5],r_[1:5])).reshape(2,-1) rbind(1:4,1:4) vstack((r_[1:5],r_[1:5])) cbind(1:4,1:4)

Desc. Bind rows Bind columns Bind slices (three-way arrays) Concatenate matrices into one vector Bind rows (from vectors) Bind columns (from vectors)

[a(:), b(:)] [1:4 ; 1:4] [1:4 ; 1:4]’

4.2
Desc.

Array creation
matlab/Octave zeros(3,5) Python zeros((3,5),Float) zeros((3,5)) ones(3,5) ones((3,5),Float) matrix(1,3,5) or array(1,c(3,5)) 1 1 1 9 9 9 1 0 0 4 0 0 8 3 4 1 1 1 9 9 9 0 1 0 0 5 0 1 5 9 1 1 1 9 9 9 0 0 1 0 0 6 6 7 2 1 1 1 9 9 9 1 1 1 9 9 9 R matrix(0,3,5) or array(0,c(3,5)) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

 filled array  filled array of integers  filled array

Any number filled array

ones(3,5)*9

matrix(9,3,5) or array(9,c(3,5))

Identity matrix

eye(3)

identity(3)

diag(1,3)

Diagonal

diag([4 5 6])

diag((4,5,6))

diag(c(4,5,6))

Magic squares; Lo Shu Empty array

magic(3) a = empty((3,3))

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4.3
Desc.

Reshape and flatten matrices
matlab/Octave reshape(1:6,3,2)’; reshape(1:6,2,3); a’(:) a(:) vech(a) Python arange(1,7).reshape(2,-1) a.setshape(2,3) R matrix(1:6,nrow=3,byrow=T) 1 4 1 2 1 1 2 5 3 4 2 4 3 6 5 6 3 2 4 5 5 3 6 6

Reshaping (rows first) Reshaping (columns first) Flatten to vector (by rows, like comics) Flatten to vector (by columns) Flatten upper triangle (by columns)

arange(1,7).reshape(-1,2).transpose() matrix(1:6,nrow=2) array(1:6,c(2,3)) as.vector(t(a)) a.flatten() or a.flatten(1) as.vector(a) a[row(a) <= col(a)]

4.4

Shared data (slicing)
matlab/Octave b = a Python b = a.copy() R b = a

Desc. Copy of a

4.5
Desc.

Indexing and accessing elements (Python: slicing)
matlab/Octave a = [ 11 12 13 14 ... 21 22 23 24 ... 31 32 33 34 ] a(2,3) a(1,:) a(:,1) a([1 3],[1 4]); a(2:end,:) a(end-1:end,:) a(1:2:end,:) Python a = array([[ 11, 12, 13, 14 ], [ 21, 22, 23, 24 ], [ 31, 32, 33, 34 ]]) a[1,2] a[0,] a[:,0] a.take([0,2]).take([0,3], axis=1) a[1:,] a[-2:,] a[::2,:] a[...,2] a[-2,-3] a(:,[1 3 4]) a.take([0,2,3],axis=1) a.diagonal(offset=0) a[,-2] a11 a31 a11 a21 a31 a11 a13 a33 a13 a23 a33 a22 a14 a34 a14 a24 a34 a33 a[-1,] R a <- rbind(c(11, 12, 13, 14), c(21, 22, 23, 24), c(31, 32, 33, 34)) a[2,3] a[1,] a[,1] a11 a21 a31 a23 a11 a11 a21 a31 a11 a31 a21 a31 a21 a31 a11 a31 a12 a22 a32 a13 a23 a33 a14 a24 a34

Input is a , array

Element , (row,col) First row First column Array as indices All, except first row Last two rows Strides: Every other row Third in last dimension (axis) All, except row,column (,) Remove one column Diagonal

a12

a13

a14

a14 a34 a22 a32 a22 a32 a12 a32 a23 a33 a23 a33 a13 a33 a24 a34 a24 a34 a14 a34

a44

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4.6
Desc.

Assignment
matlab/Octave a(:,1) = 99 a(:,1) = [99 98 97]’ a(a>90) = 90; Python a[:,0] = 99 a[:,0] = array([99,98,97]) (a>90).choose(a,90) a.clip(min=None, max=90) a.clip(min=2, max=5) R a[,1] <- 99 a[,1] <- c(99,98,97) a[a>90] <- 90

Clipping: Replace all elements over 

Clip upper and lower values

4.7

Transpose and inverse
matlab/Octave a’ a.’ or transpose(a) det(a) inv(a) pinv(a) norm(a) eig(a) svd(a) chol(a) [v,l] = eig(a) rank(a) Python a.conj().transpose() a.transpose() linalg.det(a) or linalg.inv(a) or linalg.pinv(a) norm(a) linalg.eig(a)[0] linalg.svd(a) linalg.cholesky(a) linalg.eig(a)[1] rank(a) R t(a)

Desc. Transpose Non-conjugate transpose Determinant Inverse Pseudo-inverse Norms Eigenvalues Singular values Cholesky factorization Eigenvectors Rank

det(a) solve(a) ginv(a) eigen(a)$values svd(a)$d

eigen(a)$vectors rank(a)

4.8

Sum
matlab/Octave sum(a) sum(a’) sum(sum(a)) cumsum(a) Python a.sum(axis=0) a.sum(axis=1) a.sum() a.trace(offset=0) a.cumsum(axis=0) R apply(a,2,sum) apply(a,1,sum) sum(a) apply(a,2,cumsum)

Desc. Sum of each column Sum of each row Sum of all elements Sum along diagonal Cumulative sum (columns)

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4.9
Desc.

Sorting
matlab/Octave a = [ 4 3 2 ; 2 8 6 ; 1 4 7 ] Python a = array([[4,3,2],[2,8,6],[1,4,7]]) R 4 2 1 1 3 6 1 2 4 2 2 1 1 2 4 3 8 4 2 4 7 3 4 8 3 6 4 4 8 3 2 6 7 2 4 8 2 6 7 4 8 7 7 6 2

Example data

Flat and sorted

sort(a(:))

a.ravel().sort() or

t(sort(a))

Sort each column

sort(a)

a.sort(axis=0) or msort(a)

apply(a,2,sort)

Sort each row

sort(a’)’

a.sort(axis=1)

t(apply(a,1,sort))

Sort rows (by first row) Sort, return indices Sort each column, return indices Sort each row, return indices

sortrows(a,1)

a[a[:,0].argsort(),] a.ravel().argsort() a.argsort(axis=0) a.argsort(axis=1) order(a)

4.10

Maximum and minimum
matlab/Octave max(a) max(a’) max(max(a)) [v i] = max(a) max(b,c) cummax(a) Python a.max(0) or amax(a [,axis=0]) a.max(1) or amax(a, axis=1) a.max() or maximum(b,c) a.ptp(); a.ptp(0) R apply(a,2,max) apply(a,1,max) max(a) i <- apply(a,1,which.max) pmax(b,c) apply(a,2,cummax)

Desc. max in each column max in each row max in array return indices, i pairwise max max-to-min range

4.11

Matrix manipulation
matlab/Octave fliplr(a) flipud(a) rot90(a) repmat(a,2,3) Octave: kron(ones(2,3),a) triu(a) tril(a) Python fliplr(a) or a[:,::-1] flipud(a) or a[::-1,] rot90(a) kron(ones((2,3)),a) triu(a) tril(a) R a[,4:1] a[3:1,] kronecker(matrix(1,2,3),a) a[lower.tri(a)] <- 0 a[upper.tri(a)] <- 0

Desc. Flip left-right Flip up-down Rotate  degrees Repeat matrix: [ a a a ; a a a ] Triangular, upper Triangular, lower

4.12

Equivalents to ”size”
matlab/Octave size(a) size(a,2) or length(a) length(a(:)) ndims(a) Python a.shape or a.getshape() a.shape[1] or size(a, axis=1) a.size or size(a[, axis=None]) a.ndim a.nbytes R dim(a) ncol(a) prod(dim(a)) object.size(a)

Desc. Matrix dimensions Number of columns Number of elements Number of dimensions Number of bytes used in memory

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4.13
Desc.

Matrix- and elementwise- multiplication
matlab/Octave a .* b a * b Python a * b or multiply(a,b) matrixmultiply(a,b) inner(a,b) or R a * b a %*% b 1 9 7 15 5 11 1 2 3 4 10 14 1 3 3 9 5 16 10 22 11 25 2 3 4 4 6 8 6 9 12 8 12 16 14 20 2 2 4 4 6 8 6 4 8 12 12 16

Elementwise operations Matrix product (dot product) Inner matrix vector multiplication a · b

Outer product

outer(a,b) or

outer(a,b) or a %o% b

Cross product

crossprod(a,b) or t(a) %*% b

Kronecker product Matrix division, b·a−1 Left matrix division, b−1 ·a (solve linear equations) Vector dot product Cross product

kron(a,b) a / b a \ b

kron(a,b)

kronecker(a,b)

linalg.solve(a,b) vdot(a,b) cross(a,b)

solve(a,b)

Ax = b

4.14

Find; conditional indexing
matlab/Octave find(a) [i j] = find(a) Python a.ravel().nonzero() (i,j) = a.nonzero() (i,j) = where(a!=0) v = a.compress((a!=0).flat) v = extract(a!=0,a) (a>5.5).nonzero() a.compress((a>5.5).flat) a .* (a>5.5) where(a>5.5,0,a) or a * (a>5.5) a.put(2,indices) R which(a != 0) which(a != 0, arr.ind=T)

Desc. Non-zero elements, indices Non-zero elements, array indices

Vector of non-zero values

[i j v] = find(a)

ij <- which(a != 0, arr.ind=T); v <- a[ij]

Condition, indices Return values Zero out elements above . Replace values

find(a>5.5)

which(a>5.5) ij <- which(a>5.5, arr.ind=T); v <- a[ij]

5

Multi-way arrays
matlab/Octave a = cat(3, [1 2; 1 2],[3 4; 3 4]); a(1,:,:) Python R a = array([[[1,2],[1,2]], [[3,4],[3,4]]]) a[0,...]

Desc. Define a -way array

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6

File input and output
matlab/Octave f = load(’data.txt’) f = load(’data.txt’) x = dlmread(’data.csv’, ’;’) save -ascii data.txt f Python R f = fromfile("data.txt") f <- read.table("data.txt") f = load("data.txt") f = load("data.txt") f <- read.table("data.txt") f = load(’data.csv’, delimiter=’;’) f <- read.table(file="data.csv", sep=";") save(’data.csv’, f, fmt=’%.6f’, delimiter=’;’) write(f,file="data.txt") f.tofile(file=’data.csv’, format=’%.6f’, sep=’;’) f = fromfile(file=’data.csv’, sep=’;’)

Desc. Reading from a file (d) Reading from a file (d) Reading fram a CSV file (d) Writing to a file (d) Writing to a file (d) Reading from a file (d)

7
7.1

Plotting
Basic x-y plots
matlab/Octave Python R
4 3

Desc.

2

1

0

-1

-2

-3

-4

0

20

40

60

80

100

d line plot

plot(a)

plot(a)

plot(a, type="l")
4.5

4.0

3.5

3.0

2.5

2.0 4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

d scatter plot

plot(x(:,1),x(:,2),’o’)

plot(x[:,0],x[:,1],’o’)

plot(x[,1],x[,2])
7 6

5

4

3

2

1 4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

Two graphs in one plot Overplotting: Add new plots to current

subplots Plotting symbols and color

plot(x1,y1, x2,y2) plot(x1,y1) hold on plot(x2,y2) subplot(211) plot(x,y,’ro-’)

plot(x1,y1,’bo’, x2,y2,’go’) plot(x1,y1,’o’) plot(x2,y2,’o’) show() # as normal subplot(211) plot(x,y,’ro-’)

plot(x1,y1) matplot(x2,y2,add=T)

plot(x,y,type="b",col="red")

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7.1.1

Axes and titles
matlab/Octave grid on axis equal Octave: axis(’equal’) replot axis([ 0 10 0 5 ]) title(’title’) xlabel(’x-axis’) ylabel(’y-axis’) Python grid() figure(figsize=(6,6)) R grid() plot(c(1:10,10:1), asp=1)

Desc. Turn on grid lines : aspect ratio

Set axes manually Axis labels and titles

axis([ 0, 10, 0, 5 ])

plot(x,y, xlim=c(0,10), ylim=c(0,5)) plot(1:10, main="title", xlab="x-axis", ylab="y-axis")

Insert text

text(2,25,’hello’)

7.1.2

Log plots
matlab/Octave semilogy(a) semilogx(a) loglog(a) Python semilogy(a) semilogx(a) loglog(a) R plot(x,y, log="y") plot(x,y, log="x") plot(x,y, log="xy")

Desc. logarithmic y-axis logarithmic x-axis logarithmic x and y axes

7.1.3
Desc.

Filled plots and bar plots
matlab/Octave Python R

Filled plot

fill(t,s,’b’, t,c,’g’) Octave: % fill has a bug?

fill(t,s,’b’, t,c,’g’, alpha=0.2)

plot(t,s, type="n", xlab="", ylab="") polygon(t,s, col="lightblue") polygon(t,c, col="lightgreen") stem(x[,3])
5 6 7 8 9 10 5 71 033 00113345567889 0133566677788 32674

Stem-and-Leaf plot

7.1.4

Functions
matlab/Octave f = inline(’sin(x/3) - cos(x/5)’) Python R f <- function(x) sin(x/3) - cos(x/5) f (x) = sin
1.0

Desc. Defining functions

x 3

− cos
q q q q q q q qq qqq q q q q q q q

x 5

q q q q q q q q q q q q q q q q q q q q q q q q qqqq q q q q q q q q q

0.5

q q q q q q q

q

qq

qqq

q

q

q q q q q q q q q q q q q q qq q q q q

0.0

qqqq

f (x)

q

−0.5

q q q

−1.0

q q

−2.0

−1.5

0

10

20 x

30

40

Plot a function for given range

ezplot(f,[0,40]) fplot(’sin(x/3) - cos(x/5)’,[0,40]) Octave: % no ezplot

x = arrayrange(0,40,.5) y = sin(x/3) - cos(x/5) plot(x,y, ’o’)

plot(f, xlim=c(0,40), type=’p’)

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7.2
Desc.

Polar plots
matlab/Octave theta = 0:.001:2*pi; r = sin(2*theta); Python theta = arange(0,2*pi,0.001) r = sin(2*theta) R ρ(θ) = sin(2θ)
90

135

45

180

0

225

315

270

polar(theta, rho)

polar(theta, rho)

7.3
Desc.

Histogram plots
matlab/Octave hist(randn(1000,1)) hist(randn(1000,1), -4:4) plot(sort(a)) Python R hist(rnorm(1000)) hist(rnorm(1000), breaks= -4:4) hist(rnorm(1000), breaks=c(seq(-5,0,0.25), seq(0.5,5,0.5)), freq=F) plot(apply(a,1,sort),type="l")

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7.4
7.4.1
Desc.

3d data
Contour and image plots
matlab/Octave Python R
2

0.0

1

0.4

0.2
-0.2 -0.4

0.8

0.

6

0.6

-0.6

0

0.8

1.0

-1

-0.2

-2

-2

-1

0

1

2

Contour plot

contour(z)

levels, colls = contour(Z, V, contour(z) origin=’lower’, extent=(-3,3,-3,3)) clabel(colls, levels, inline=1, fmt=’%1.1f’, fontsize=10)
2

1

0

-1

-2

-2

-1

0

1

2

Filled contour plot

contourf(z); colormap(gray)

contourf(Z, V, cmap=cm.gray, origin=’lower’, extent=(-3,3,-3,3))

filled.contour(x,y,z, nlevels=7, color=gray.colors)

Plot image data

image(z) colormap(gray)

im = imshow(Z, interpolation=’bilinear’, origin=’lower’, extent=(-3,3,-3,3))

image(z, col=gray.colors(256))

2

0.0

1

0.4

0.2
-0.2 -0.4

0.8

0.

6

0.6

-0.6

0

0.8

1.0

-1

-0.2

-2

-2

-1

0

1

2

Image with contours Direction field vectors

quiver()

# imshow() and contour() as above quiver()

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7.4.2
Desc.

Perspective plots of surfaces over the x-y plane
matlab/Octave n=-2:.1:2; [x,y] = meshgrid(n,n); z=x.*exp(-x.^2-y.^2); Python n=arrayrange(-2,2,.1) [x,y] = meshgrid(n,n) z = x*power(math.e,-x**2-y**2) R f <- function(x,y) x*exp(-x^2-y^2) n <- seq(-2,2, length=40) z <- outer(n,n,f) f (x, y) = xe−x
2 −y 2

0.4

0.2 0.0 2 −0.2 1 −0.4 −2 −1 0 −1 1 2 −2 0

x

Mesh plot

mesh(z)

persp(x,y,z, theta=30, phi=30, expand=0.6, ticktype=’detailed’)

0.4 0.2 0.0 −0.2 1 −0.4 −2 −1 0 −1 1 −2

y
2 0
y

z
z

x

2

Surface plot

surf(x,y,z) or surfl(x,y,z) Octave: % no surfl()

persp(x,y,z, theta=30, phi=30, expand=0.6, col=’lightblue’, shade=0.75, ltheta=120, ticktype=’detailed’)

7.4.3
Desc.

Scatter (cloud) plots
matlab/Octave Python R
’icc-gamut.csv’

80 60 40 20 0 -20 -40 -60 -80 70 80 60 40 20 0 -20 -40 10 -60 0 20 30 40 50 60

100 90 80

d scatter plot

plot3(x,y,z,’k+’)

cloud(z~x*y)

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7.5

Save plot to a graphics file
matlab/Octave plot(1:10) print -depsc2 foo.eps Octave: gset output "foo.eps" gset terminal postscript eps plot(1:10) Python savefig(’foo.eps’) R postscript(file="foo.eps") plot(1:10) dev.off()

Desc. PostScript

PDF SVG (vector graphics for www) PNG (raster graphics)

print -dpng foo.png

savefig(’foo.pdf’) savefig(’foo.svg’) savefig(’foo.png’)

pdf(file=’foo.pdf’) devSVG(file=’foo.svg’) png(filename = "Rplot%03d.png"

8
8.1

Data analysis
Set membership operators
matlab/Octave a = [ 1 2 2 5 2 ]; b = [ 2 3 4 ]; Python a = array([1,2,2,5,2]) b = array([2,3,4]) a = set([1,2,2,5,2]) b = set([2,3,4]) unique1d(a) unique(a) set(a) R a <- c(1,2,2,5,2) b <- c(2,3,4)

Desc. Create sets

Set unique

unique(a)

unique(a)

1

2

5

Set union

union(a,b)

union1d(a,b) a.union(b)

union(a,b)

Set intersection

intersect(a,b)

intersect1d(a) a.intersection(b)

intersect(a,b)

Set difference

setdiff(a,b)

setdiff1d(a,b) a.difference(b)

setdiff(a,b)

Set exclusion True for set member

setxor(a,b) ismember(2,a)

setxor1d(a,b) a.symmetric_difference(b) 2 in a setmember1d(2,a) contains(a,2)

setdiff(union(a,b),intersect(a,b)) is.element(2,a) or 2 %in% a

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8.2

Statistics
matlab/Octave mean(a) median(a) std(a) var(a) corr(x,y) cov(x,y) Python a.mean(axis=0) mean(a [,axis=0]) median(a) or median(a [,axis=0]) a.std(axis=0) or std(a [,axis=0]) a.var(axis=0) or var(a) correlate(x,y) or corrcoef(x,y) cov(x,y) R apply(a,2,mean) apply(a,2,median) apply(a,2,sd) apply(a,2,var) cor(x,y) cov(x,y)

Desc. Average Median Standard deviation Variance Correlation coefficient Covariance

8.3

Interpolation and regression
matlab/Octave z = polyval(polyfit(x,y,1),x) plot(x,y,’o’, x,z ,’-’) a = x\y polyfit(x,y,3) Python (a,b) = polyfit(x,y,1) plot(x,y,’o’, x,a*x+b,’-’) linalg.lstsq(x,y) polyfit(x,y,3) R z <- lm(y~x) plot(x,y) abline(z) solve(a,b)

Desc. Straight line fit

Linear least squares y = ax + b Polynomial fit

8.4
8.4.1

Non-linear methods
Polynomials, root finding
matlab/Octave roots([1 -1 -1]) f = inline(’1/x - (x-1)’) fzero(f,1) solve(’1/x = x-1’) polyval([1 2 1 2],1:10) Python poly() roots() R polyroot(c(1,-1,-1)) x2 − x − 1 = 0 1 f (x) = x − (x − 1)
1 x

Desc. Polynomial Find zeros of polynomial Find a zero near x = 1 Solve symbolic equations Evaluate polynomial

=x−1

polyval(array([1,2,1,2]),arange(1,11))

8.4.2

Differential equations
matlab/Octave diff(a) Python diff(x, n=1, axis=0) R

Desc. Discrete difference function and approximate derivative Solve differential equations

8.5

Fourier analysis
matlab/Octave fft(a) ifft(a) Python fft(a) or ifft(a) or convolve(x,y) R fft(a) fft(a, inverse=TRUE)

Desc. Fast fourier transform Inverse fourier transform Linear convolution

9

Symbolic algebra; calculus
matlab/Octave factor() Python R

Desc. Factorization

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10

Programming
matlab/Octave .m % Octave: % or # % must be in MATLABPATH Octave: % must be in LOADPATH string=’a=234’; eval(string) Python .py # from pylab import * string="a=234" eval(string) R .R # library(RSvgDevice) string <- "a <- 234" eval(parse(text=string))

Desc. Script file extension Comment symbol (rest of line) Import library functions Eval

10.1

Loops
matlab/Octave for i=1:5; disp(i); end for i=1:5 disp(i) disp(i*2) end Python for i in range(1,6): print(i) for i in range(1,6): print(i) print(i*2) R for(i in 1:5) print(i) for(i in 1:5) { print(i) print(i*2) }

Desc. for-statement Multiline for statements

10.2

Conditionals
matlab/Octave if 1>0 a=100; end if 1>0 a=100; else a=0; end Python if 1>0: a=100 R if (1>0) a <- 100 ifelse(a>0,a,0) a > 0?a : 0

Desc. if-statement if-else-statement Ternary operator (if?true:false)

10.3

Debugging
matlab/Octave ans whos or who clear x or clear [all] disp(a) Python R .Last.value objects() rm(x) print(a)

Desc. Most recent evaluated expression List variables loaded into memory Clear variable x from memory Print

print a

10.4

Working directory and OS
matlab/Octave dir or ls what pwd cd foo !notepad Octave: system("notepad") Python os.listdir(".") grep.grep("*.py") os.getcwd() os.chdir(’foo’) os.system(’notepad’) os.popen(’notepad’) R list.files() or dir() list.files(pattern="\.r$") getwd() setwd(’foo’) system("notepad")

Desc. List files in directory List script files in directory Displays the current working directory Change working directory Invoke a System Command

 This document is still draft quality. Most shown d plots are made using Matplotlib, and d plots using R and Gnuplot, provided as examples only.  Version numbers and download url for software used: Python .., http://www.python.org/; NumPy .., http://numeric.scipy.org/; Matplotlib ., http://matplotlib.sf.net/; IPython ..,

http://ipython.scipy.org/; R .., http://www.r-project.org/; Octave .., http://www.octave.org/; Scilab ., http://www.scilab.org/; Gnuplot ., http://www.gnuplot.info/.  For referencing: Gundersen, Vidar Bronken. MATLAB commands in numerical Python (Oslo/Norway, ), available from: http://mathesaurus.sf.net/  Contributions are appreciated: The best way to do this is to edit the xml and submit patches to our tracker or forums.


				
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