Matlab python-

MATLAB commands in numerical Python (NumPy) 1
Vidar Bronken Gundersen /mathesaurus.sf.net
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
Desc. matlab/Octave Python R
Browse help interactively doc
Octave: help -i % browse with Info
help() help.start()
Help on using help help help or doc doc help help()
Help for a function help plot help(plot) or ?plot help(plot) or ?plot
Help for a toolbox/library package help splines or doc splines help(pylab) help(package=’splines’)
Demonstration examples demo demo()
Example using a function example(plot)
1.1 Searching available documentation
Search help ﬁles lookfor plot help.search(’plot’)
Find objects by partial name apropos(’plot’)
List available packages help help(); modules [Numeric] library()
Locate functions which plot help(plot) find(plot)
List available methods for a function methods(plot)
1.2 Using interactively
Start session Octave: octave -q ipython -pylab Rgui
Auto completion Octave: TAB or M-? TAB
Run code from ﬁle foo(.m) execfile(’foo.py’) or run foo.py source(’foo.R’)
Command history Octave: history hist -n history()
Save command history diary on [..] diary off savehistory(file=".Rhistory")
End session exit or quit CTRL-D
CTRL-Z # windows
sys.exit()
q(save=’no’)
2 Operators
Help on operator syntax help - help(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 ..).

2.1 Arithmetic operators
Assignment; deﬁning a number a=1; b=2; a=1; b=1 a<-1; b<-2
Addition a + b a + b or add(a,b) a + b
Subtraction a - b a - b or subtract(a,b) a - b
Multiplication a * b a * b or multiply(a,b) a * b
Division a / b a / b or divide(a,b) a / b
Power, ab
a .^ b a ** b
power(a,b)
pow(a,b)
a ^ b
Remainder rem(a,b) a % b
remainder(a,b)
fmod(a,b)
a %% b
Integer division a %/% b
In place operation to save array creation
overhead
Octave: a+=1 a+=b or add(a,b,a)
Factorial, n! factorial(a) factorial(a)
2.2 Relational operators
Equal a == b a == b or equal(a,b) a == b
Less than a < b a < b or less(a,b) a < b
Greater than a > b a > b or greater(a,b) a > b
Less than or equal a <= b a <= b or less_equal(a,b) a <= b
Greater than or equal a >= b a >= b or greater_equal(a,b) a >= b
Not Equal a ~= b a != b or not_equal(a,b) a != b
2.3 Logical operators
Short-circuit logical AND a && b a and b a && b
Short-circuit logical OR a || b a or b a || b
Element-wise logical AND a & b or and(a,b) logical_and(a,b) or a and b a & b
Element-wise logical OR a | b or or(a,b) logical_or(a,b) or a or b a | b
Logical EXCLUSIVE OR xor(a, b) logical_xor(a,b) xor(a, b)
Logical NOT ~a or not(a)
Octave: ~a or !a
logical_not(a) or not a !a
True if any element is nonzero any(a)
True if all elements are nonzero all(a)
2.4 root and logarithm
Square root sqrt(a) math.sqrt(a) sqrt(a)
√
a
Logarithm, base e (natural) log(a) math.log(a) log(a) ln a = loge a
Logarithm, base  log10(a) math.log10(a) log10(a) log10 a
Logarithm, base  (binary) log2(a) math.log(a, 2) log2(a) log2 a
Exponential function exp(a) math.exp(a) exp(a) ea

2.5 Round off
Round round(a) around(a) or math.round(a) round(a)
Round up ceil(a) ceil(a) ceil(a)
Round down floor(a) floor(a) floor(a)
Round towards zero fix(a) fix(a)
2.6 Mathematical constants
π = 3.141592 pi math.pi pi
e = 2.718281 exp(1) math.e or math.exp(1) exp(1)
2.6.1 Missing values; IEEE-754 floating point status flags
Not a Number NaN nan
Infinity, ∞ Inf inf
Infinity, +∞ plus_inf
Infinity, −∞ minus_inf
Plus zero, +0 plus_zero
Minus zero, −0 minus_zero
2.7 Complex numbers
Imaginary unit i z = 1j 1i i =
√
−1
A complex number, 3 + 4i z = 3+4i z = 3+4j or z = complex(3,4) z <- 3+4i
Absolute value (modulus) abs(z) abs(3+4j) abs(3+4i) or Mod(3+4i)
Real part real(z) z.real Re(3+4i)
Imaginary part imag(z) z.imag Im(3+4i)
Argument arg(z) Arg(3+4i)
Complex conjugate conj(z) z.conj(); z.conjugate() Conj(3+4i)
2.8 Trigonometry
Arctangent, arctan(b/a) atan(a,b) atan2(b,a) atan2(b,a)
Hypotenus; Euclidean distance hypot(x,y) x2 + y2
2.9 Generate random numbers
Uniform distribution rand(1,10) random.random((10,))
random.uniform((10,))
runif(10)
Uniform: Numbers between  and  2+5*rand(1,10) random.uniform(2,7,(10,)) runif(10, min=2, max=7)
Uniform: , array rand(6) random.uniform(0,1,(6,6)) matrix(runif(36),6)
Normal distribution randn(1,10) random.standard_normal((10,)) rnorm(10)

3 Vectors
Row vector, 1 × n-matrix a=[2 3 4 5]; a=array([2,3,4,5]) a <- c(2,3,4,5)
Column vector, m × 1-matrix adash=[2 3 4 5]’; array([2,3,4,5])[:,NewAxis]
array([2,3,4,5]).reshape(-1,1)
r_[1:10,’c’]
adash <- t(c(2,3,4,5))
3.1 Sequences
,,, ... , 1:10 arange(1,11, dtype=Float)
range(1,11)
seq(10) or 1:10
.,.,., ... ,. 0:9 arange(10.) seq(0,length=10)
,,, 1:3:10 arange(1,11,3) seq(1,10,by=3)
,,, ... , 10:-1:1 arange(10,0,-1) seq(10,1) or 10:1
,,, 10:-3:1 arange(10,0,-3) seq(from=10,to=1,by=-3)
Linearly spaced vector of n= points linspace(1,10,7) linspace(1,10,7) seq(1,10,length=7)
Reverse reverse(a) a[::-1] or rev(a)
Set all values to same scalar value a(:) = 3 a.fill(3), a[:] = 3
3.2 Concatenation (vectors)
Concatenate two vectors [a a] concatenate((a,a)) c(a,a)
[1:4 a] concatenate((range(1,5),a), axis=1) c(1:4,a)
3.3 Repeating
  ,    [a a] concatenate((a,a)) rep(a,times=2)
  ,   ,    a.repeat(3) or rep(a,each=3)
,  ,    a.repeat(a) or rep(a,a)
3.4 Miss those elements out
miss the ﬁrst element a(2:end) a[1:] a[-1]
miss the tenth element a([1:9]) a[-10]
miss ,,, ... a[-seq(1,50,3)]
last element a(end) a[-1]
last two elements a(end-1:end) a[-2:]
3.5 Maximum and minimum
pairwise max max(a,b) maximum(a,b) pmax(a,b)
max of all values in two vectors max([a b]) concatenate((a,b)).max() max(a,b)
[v,i] = max(a) v,i = a.max(0),a.argmax(0) v <- max(a) ; i <- which.max(a)

3.6 Vector multiplication
Multiply two vectors a.*a a*a a*a
Vector dot product, u · v dot(u,v) dot(u,v)
4 Matrices
Define a matrix a = [2 3;4 5] a = array([[2,3],[4,5]]) rbind(c(2,3),c(4,5))
array(c(2,3,4,5), dim=c(2,2))
2 3
4 5
4.1 Concatenation (matrices); rbind and cbind
Bind rows [a ; b] concatenate((a,b), axis=0)
vstack((a,b))
rbind(a,b)
Bind columns [a , b] concatenate((a,b), axis=1)
hstack((a,b))
cbind(a,b)
Bind slices (three-way arrays) concatenate((a,b), axis=2)
dstack((a,b))
Concatenate matrices into one vector [a(:), b(:)] concatenate((a,b), axis=None)
Bind rows (from vectors) [1:4 ; 1:4] concatenate((r_[1:5],r_[1:5])).reshape(2,-1)
vstack((r_[1:5],r_[1:5]))
rbind(1:4,1:4)
Bind columns (from vectors) [1:4 ; 1:4]’ cbind(1:4,1:4)
4.2 Array creation
 filled array zeros(3,5) zeros((3,5),Float) 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 of integers zeros((3,5))
 filled array ones(3,5) ones((3,5),Float) matrix(1,3,5) or array(1,c(3,5))
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
Any number filled array ones(3,5)*9 matrix(9,3,5) or array(9,c(3,5))
9 9 9 9 9
9 9 9 9 9
9 9 9 9 9
Identity matrix eye(3) identity(3) diag(1,3)
1 0 0
0 1 0
0 0 1
Diagonal diag([4 5 6]) diag((4,5,6)) diag(c(4,5,6))
4 0 0
0 5 0
0 0 6
Magic squares; Lo Shu magic(3)
8 1 6
3 5 7
4 9 2
Empty array a = empty((3,3))

4.3 Reshape and flatten matrices
Reshaping (rows first) reshape(1:6,3,2)’; arange(1,7).reshape(2,-1)
a.setshape(2,3)
matrix(1:6,nrow=3,byrow=T)
1 2 3
4 5 6
Reshaping (columns first) reshape(1:6,2,3); arange(1,7).reshape(-1,2).transpose() matrix(1:6,nrow=2)
array(1:6,c(2,3))
1 3 5
2 4 6
Flatten to vector (by rows, like comics) a’(:) a.flatten() or as.vector(t(a)) 1 2 3 4 5 6
Flatten to vector (by columns) a(:) a.flatten(1) as.vector(a) 1 4 2 5 3 6
Flatten upper triangle (by columns) vech(a) a[row(a) <= col(a)]
4.4 Shared data (slicing)
Copy of a b = a b = a.copy() b = a
4.5 Indexing and accessing elements (Python: slicing)
Input is a , array a = [ 11 12 13 14 ...
21 22 23 24 ...
31 32 33 34 ]
a = array([[ 11, 12, 13, 14 ],
[ 21, 22, 23, 24 ],
[ 31, 32, 33, 34 ]])
a <- rbind(c(11, 12, 13, 14),
c(21, 22, 23, 24),
c(31, 32, 33, 34))
a11 a12 a13 a14
a21 a22 a23 a24
a31 a32 a33 a34
Element , (row,col) a(2,3) a[1,2] a[2,3] a23
First row a(1,:) a[0,] a[1,] a11 a12 a13 a14
First column a(:,1) a[:,0] a[,1]
a11
a21
a31
Array as indices a([1 3],[1 4]); a.take([0,2]).take([0,3], axis=1)
a11 a14
a31 a34
All, except first row a(2:end,:) a[1:,] a[-1,]
a21 a22 a23 a24
a31 a32 a33 a34
Last two rows a(end-1:end,:) a[-2:,]
a21 a22 a23 a24
a31 a32 a33 a34
Strides: Every other row a(1:2:end,:) a[::2,:]
a11 a12 a13 a14
a31 a32 a33 a34
Third in last dimension (axis) a[...,2]
All, except row,column (,) a[-2,-3]
a11 a13 a14
a31 a33 a34
Remove one column a(:,[1 3 4]) a.take([0,2,3],axis=1) a[,-2]
a11 a13 a14
a21 a23 a24
a31 a33 a34
Diagonal a.diagonal(offset=0) a11 a22 a33 a44

4.6 Assignment
a(:,1) = 99 a[:,0] = 99 a[,1] <- 99
a(:,1) = [99 98 97]’ a[:,0] = array([99,98,97]) a[,1] <- c(99,98,97)
Clipping: Replace all elements over  a(a>90) = 90; (a>90).choose(a,90)
a.clip(min=None, max=90)
a[a>90] <- 90
Clip upper and lower values a.clip(min=2, max=5)
4.7 Transpose and inverse
Transpose a’ a.conj().transpose() t(a)
Non-conjugate transpose a.’ or transpose(a) a.transpose()
Determinant det(a) linalg.det(a) or det(a)
Inverse inv(a) linalg.inv(a) or solve(a)
Pseudo-inverse pinv(a) linalg.pinv(a) ginv(a)
Norms norm(a) norm(a)
Eigenvalues eig(a) linalg.eig(a)[0] eigen(a)$values
Singular values svd(a) linalg.svd(a) svd(a)$d
Cholesky factorization chol(a) linalg.cholesky(a)
Eigenvectors [v,l] = eig(a) linalg.eig(a)[1] eigen(a)$vectors
Rank rank(a) rank(a) rank(a)
4.8 Sum
Sum of each column sum(a) a.sum(axis=0) apply(a,2,sum)
Sum of each row sum(a’) a.sum(axis=1) apply(a,1,sum)
Sum of all elements sum(sum(a)) a.sum() sum(a)
Sum along diagonal a.trace(offset=0)
Cumulative sum (columns) cumsum(a) a.cumsum(axis=0) apply(a,2,cumsum)

4.9 Sorting
Example data a = [ 4 3 2 ; 2 8 6 ; 1 4 7 ] a = array([[4,3,2],[2,8,6],[1,4,7]])
4 3 2
2 8 6
1 4 7
Flat and sorted sort(a(:)) a.ravel().sort() or t(sort(a))
1 2 2
3 4 4
6 7 8
Sort each column sort(a) a.sort(axis=0) or msort(a) apply(a,2,sort)
1 3 2
2 4 6
4 8 7
Sort each row sort(a’)’ a.sort(axis=1) t(apply(a,1,sort))
2 3 4
2 6 8
1 4 7
Sort rows (by ﬁrst row) sortrows(a,1) a[a[:,0].argsort(),]
1 4 7
2 8 6
4 3 2
Sort, return indices a.ravel().argsort() order(a)
Sort each column, return indices a.argsort(axis=0)
Sort each row, return indices a.argsort(axis=1)
4.10 Maximum and minimum
max in each column max(a) a.max(0) or amax(a [,axis=0]) apply(a,2,max)
max in each row max(a’) a.max(1) or amax(a, axis=1) apply(a,1,max)
max in array max(max(a)) a.max() or max(a)
return indices, i [v i] = max(a) i <- apply(a,1,which.max)
pairwise max max(b,c) maximum(b,c) pmax(b,c)
cummax(a) apply(a,2,cummax)
max-to-min range a.ptp(); a.ptp(0)
4.11 Matrix manipulation
Flip left-right fliplr(a) fliplr(a) or a[:,::-1] a[,4:1]
Flip up-down flipud(a) flipud(a) or a[::-1,] a[3:1,]
Rotate  degrees rot90(a) rot90(a)
Repeat matrix: [ a a a ; a a a ] repmat(a,2,3)
Octave: kron(ones(2,3),a)
kron(ones((2,3)),a) kronecker(matrix(1,2,3),a)
Triangular, upper triu(a) triu(a) a[lower.tri(a)] <- 0
Triangular, lower tril(a) tril(a) a[upper.tri(a)] <- 0
4.12 Equivalents to ”size”
Matrix dimensions size(a) a.shape or a.getshape() dim(a)
Number of columns size(a,2) or length(a) a.shape[1] or size(a, axis=1) ncol(a)
Number of elements length(a(:)) a.size or size(a[, axis=None]) prod(dim(a))
Number of dimensions ndims(a) a.ndim
Number of bytes used in memory a.nbytes object.size(a)

4.13 Matrix- and elementwise- multiplication
Elementwise operations a .* b a * b or multiply(a,b) a * b
1 5
9 16
Matrix product (dot product) a * b matrixmultiply(a,b) a %*% b
7 10
15 22
Inner matrix vector multiplication a · b inner(a,b) or
5 11
11 25
Outer product outer(a,b) or outer(a,b) or a %o% b
1 2 3 4
2 4 6 8
3 6 9 12
4 8 12 16
Cross product crossprod(a,b) or t(a) %*% b
10 14
14 20
Kronecker product kron(a,b) kron(a,b) kronecker(a,b)
1 2 2 4
3 4 6 8
3 6 4 8
9 12 12 16
Matrix division, b·a−1
a / b
Left matrix division, b−1
·a
(solve linear equations)
a b linalg.solve(a,b) solve(a,b) Ax = b
Vector dot product vdot(a,b)
Cross product cross(a,b)
4.14 Find; conditional indexing
Non-zero elements, indices find(a) a.ravel().nonzero() which(a != 0)
Non-zero elements, array indices [i j] = find(a) (i,j) = a.nonzero()
(i,j) = where(a!=0)
which(a != 0, arr.ind=T)
Vector of non-zero values [i j v] = find(a) v = a.compress((a!=0).flat)
v = extract(a!=0,a)
ij <- which(a != 0, arr.ind=T); v <- a[ij]
Condition, indices find(a>5.5) (a>5.5).nonzero() which(a>5.5)
Return values a.compress((a>5.5).flat) ij <- which(a>5.5, arr.ind=T); v <- a[ij]
Zero out elements above . a .* (a>5.5) where(a>5.5,0,a) or a * (a>5.5)
Replace values a.put(2,indices)
5 Multi-way arrays
Deﬁne a -way array a = cat(3, [1 2; 1 2],[3 4; 3 4]); a = array([[[1,2],[1,2]], [[3,4],[3,4]]])
a(1,:,:) a[0,...]

6 File input and output
Reading from a file (d) f = load(’data.txt’) f = fromfile("data.txt")
f = load("data.txt")
f <- read.table("data.txt")
Reading from a file (d) f = load(’data.txt’) f = load("data.txt") f <- read.table("data.txt")
Reading fram a CSV file (d) x = dlmread(’data.csv’, ’;’) f = load(’data.csv’, delimiter=’;’) f <- read.table(file="data.csv", sep=";")
Writing to a file (d) save -ascii data.txt f save(’data.csv’, f, fmt=’%.6f’, delimiter=’;’)write(f,file="data.txt")
Writing to a file (d) f.tofile(file=’data.csv’, format=’%.6f’, sep=’;’)
Reading from a file (d) f = fromfile(file=’data.csv’, sep=’;’)
7 Plotting
7.1 Basic x-y plots
d line plot plot(a) plot(a) plot(a, type="l")
0 20 40 60 80 100
-4
-3
-2
-1
0
1
2
3
4
d scatter plot plot(x(:,1),x(:,2),’o’) plot(x[:,0],x[:,1],’o’) plot(x[,1],x[,2])
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
2.0
2.5
3.0
3.5
4.0
4.5
Two graphs in one plot plot(x1,y1, x2,y2) plot(x1,y1,’bo’, x2,y2,’go’)
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
1
2
3
4
5
6
7
Overplotting: Add new plots to current plot(x1,y1)
hold on
plot(x2,y2)
plot(x1,y1,’o’)
plot(x2,y2,’o’)
show() # as normal
plot(x1,y1)
matplot(x2,y2,add=T)
subplots subplot(211) subplot(211)
Plotting symbols and color plot(x,y,’ro-’) plot(x,y,’ro-’) plot(x,y,type="b",col="red")

7.1.1 Axes and titles
Turn on grid lines grid on grid() grid()
: aspect ratio axis equal
Octave:
axis(’equal’)
replot
figure(figsize=(6,6)) plot(c(1:10,10:1), asp=1)
Set axes manually axis([ 0 10 0 5 ]) axis([ 0, 10, 0, 5 ]) plot(x,y, xlim=c(0,10), ylim=c(0,5))
Axis labels and titles title(’title’)
xlabel(’x-axis’)
ylabel(’y-axis’)
plot(1:10, main="title",
xlab="x-axis", ylab="y-axis")
Insert text text(2,25,’hello’)
7.1.2 Log plots
logarithmic y-axis semilogy(a) semilogy(a) plot(x,y, log="y")
logarithmic x-axis semilogx(a) semilogx(a) plot(x,y, log="x")
logarithmic x and y axes loglog(a) loglog(a) plot(x,y, log="xy")
7.1.3 Filled plots and bar plots
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-and-Leaf plot stem(x[,3])
5 5
6 71
7 033
8 00113345567889
9 0133566677788
10 32674
7.1.4 Functions
Deﬁning functions f = inline(’sin(x/3) - cos(x/5)’) f <- function(x) sin(x/3) - cos(x/5) f(x) = sin x
3 − cos x
5
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’)
q
q
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q
0 10 20 30 40
−2.0−1.5−1.0−0.50.00.51.0
x
f(x)

7.2 Polar plots
theta = 0:.001:2*pi;
r = sin(2*theta);
theta = arange(0,2*pi,0.001)
r = sin(2*theta)
ρ(θ) = sin(2θ)
polar(theta, rho) polar(theta, rho)
0
45
90
135
180
225
270
315
7.3 Histogram plots
hist(randn(1000,1)) hist(rnorm(1000))
hist(randn(1000,1), -4:4) 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(sort(a)) plot(apply(a,1,sort),type="l")

7.4 3d data
7.4.1 Contour and image plots
Contour plot contour(z) levels, colls = contour(Z, V,
origin=’lower’, extent=(-3,3,-3,3))
clabel(colls, levels, inline=1,
fmt=’%1.1f’, fontsize=10)
contour(z)
-2 -1 0 1 2
-2
-1
0
1
2
-0.6
-0.4
-0.2
-0.2
0.0
0.2
0.4
0.6
0.6
0.8
0.8
1.0
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)
-2 -1 0 1 2
-2
-1
0
1
2
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))
Image with contours # imshow() and contour() as above
-2 -1 0 1 2
-2
-1
0
1
2
-0.6
-0.4
-0.2
-0.2
0.0
0.2
0.4
0.6
0.6
0.8
0.8
1.0
Direction ﬁeld vectors quiver() quiver()

7.4.2 Perspective plots of surfaces over the x-y plane
n=-2:.1:2;
[x,y] = meshgrid(n,n);
z=x.*exp(-x.^2-y.^2);
n=arrayrange(-2,2,.1)
[x,y] = meshgrid(n,n)
z = x*power(math.e,-x**2-y**2)
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−x2−y2
Mesh plot mesh(z) persp(x,y,z,
theta=30, phi=30, expand=0.6,
ticktype=’detailed’)
x
−2
−1
0
1
2
y
−2
−1
0
1
2
z
−0.4
−0.2
0.0
0.2
0.4
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’)
x
−2
−1
0
1
2
y
−2
−1
0
1
2
z
−0.4
−0.2
0.0
0.2
0.4
7.4.3 Scatter (cloud) plots
d scatter plot plot3(x,y,z,’k+’) cloud(z~x*y)
0
10
20
30
40
50
60
70
80
90
100
-60
-40
-20
0
20
40
60
80
-80
-60
-40
-20
0
20
40
60
80
’icc-gamut.csv’

7.5 Save plot to a graphics ﬁle
PostScript plot(1:10)
print -depsc2 foo.eps
Octave:
gset output "foo.eps"
gset terminal postscript eps
plot(1:10)
savefig(’foo.eps’) postscript(file="foo.eps")
plot(1:10)
dev.off()
PDF savefig(’foo.pdf’) pdf(file=’foo.pdf’)
SVG (vector graphics for www) savefig(’foo.svg’) devSVG(file=’foo.svg’)
PNG (raster graphics) print -dpng foo.png savefig(’foo.png’) png(filename = "Rplot%03d.png"
8 Data analysis
8.1 Set membership operators
Create sets a = [ 1 2 2 5 2 ];
b = [ 2 3 4 ];
a = array([1,2,2,5,2])
b = array([2,3,4])
a = set([1,2,2,5,2])
b = set([2,3,4])
a <- c(1,2,2,5,2)
b <- c(2,3,4)
Set unique unique(a) unique1d(a)
unique(a)
set(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 setxor(a,b) setxor1d(a,b)
a.symmetric_difference(b)
setdiff(union(a,b),intersect(a,b))
True for set member ismember(2,a) 2 in a
setmember1d(2,a)
contains(a,2)
is.element(2,a) or 2 %in% a

8.2 Statistics
Average mean(a) a.mean(axis=0)
mean(a [,axis=0])
apply(a,2,mean)
Median median(a) median(a) or median(a [,axis=0]) apply(a,2,median)
Standard deviation std(a) a.std(axis=0) or std(a [,axis=0]) apply(a,2,sd)
Variance var(a) a.var(axis=0) or var(a) apply(a,2,var)
Correlation coefficient corr(x,y) correlate(x,y) or corrcoef(x,y) cor(x,y)
Covariance cov(x,y) cov(x,y) cov(x,y)
8.3 Interpolation and regression
Straight line fit z = polyval(polyfit(x,y,1),x)
plot(x,y,’o’, x,z ,’-’)
(a,b) = polyfit(x,y,1)
plot(x,y,’o’, x,a*x+b,’-’)
z <- lm(y~x)
plot(x,y)
abline(z)
Linear least squares y = ax + b a = xy linalg.lstsq(x,y) solve(a,b)
Polynomial fit polyfit(x,y,3) polyfit(x,y,3)
8.4 Non-linear methods
8.4.1 Polynomials, root finding
Polynomial poly()
Find zeros of polynomial roots([1 -1 -1]) roots() polyroot(c(1,-1,-1)) x2
− x − 1 = 0
Find a zero near x = 1 f = inline(’1/x - (x-1)’)
fzero(f,1)
f(x) = 1
x − (x − 1)
Solve symbolic equations solve(’1/x = x-1’) 1
x = x − 1
Evaluate polynomial polyval([1 2 1 2],1:10) polyval(array([1,2,1,2]),arange(1,11))
8.4.2 Differential equations
Discrete difference function and approxi-
mate derivative
diff(a) diff(x, n=1, axis=0)
Solve differential equations
8.5 Fourier analysis
Fast fourier transform fft(a) fft(a) or fft(a)
Inverse fourier transform ifft(a) ifft(a) or fft(a, inverse=TRUE)
Linear convolution convolve(x,y)
9 Symbolic algebra; calculus
Factorization factor()

10 Programming
Script file extension .m .py .R
Comment symbol (rest of line) %
Octave: % or #
# #
Import library functions % must be in MATLABPATH
Octave: % must be in LOADPATH
from pylab import * library(RSvgDevice)
Eval string=’a=234’;
eval(string)
string="a=234"
eval(string)
string <- "a <- 234"
eval(parse(text=string))
10.1 Loops
for-statement for i=1:5; disp(i); end for i in range(1,6): print(i) for(i in 1:5) print(i)
Multiline for statements for i=1:5
disp(i)
disp(i*2)
end
for i in range(1,6):
print(i)
print(i*2)
for(i in 1:5) {
print(i)
print(i*2)
}
10.2 Conditionals
if-statement if 1>0 a=100; end if 1>0: a=100 if (1>0) a <- 100
if-else-statement if 1>0 a=100; else a=0; end
Ternary operator (if?true:false) ifelse(a>0,a,0) a > 0?a : 0
10.3 Debugging
Most recent evaluated expression ans .Last.value
List variables loaded into memory whos or who objects()
Clear variable x from memory clear x or clear [all] rm(x)
Print disp(a) print a print(a)
10.4 Working directory and OS
List files in directory dir or ls os.listdir(".") list.files() or dir()
List script files in directory what grep.grep("*.py") list.files(pattern=".r$")
Displays the current working directory pwd os.getcwd() getwd()
Change working directory cd foo os.chdir(’foo’) setwd(’foo’)
Invoke a System Command !notepad
Octave: system("notepad")
os.system(’notepad’)
os.popen(’notepad’)
system("notepad")
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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