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MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
IDL commands in numerical Python
c
Copyright 
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.
Contributor: Gary Ruben
The idea of this document (and the corresponding xml instance) is to provide a quick reference for switching from idl
to an open-source environment, such as gdl, Python, R or Octave and Gnuplot for numeric processing and data visualisation.
Time-stamp: --T:: vidar
1
Help
Desc.
Browse help interactively
IDL
?
Python
help()
Help on using help
Help for a function
Help for a toolbox/library package
Demonstration examples
?help
?plot or man,’plot
help
help(plot) or ?plot
help(pylab)
1.1
Searching available documentation
Desc.
Search help files
List available packages
Locate functions
1.2
IDL
Python
help(); modules [Numeric]
help(plot)
matlab/Octave
lookfor plot
help
which plot
Using interactively
Desc.
Start session
Auto completion
Run code from file
Command history
Save command history
End session
2
demo
matlab/Octave
doc
Octave: help -i % browse with Info
help help or doc doc
help plot
help splines or doc splines
demo
IDL
idlde
@"foo.idlbatch" or .run ’foo.pro’
help,/rec
journal,’IDLhistory’
exit or CTRL-D
Python
ipython -pylab
TAB
execfile(’foo.py’) or run foo.py
hist -n
CTRL-D
CTRL-Z # windows
sys.exit()
matlab/Octave
Octave: octave -q
Octave: TAB or M-?
foo(.m)
Octave: history
diary on [..] diary off
exit or quit
Operators
Desc.
Help on operator syntax
IDL
Python
matlab/Octave
help -
 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 ..); Greenfield, Jedrzejewski & Laidler. Using Python for Interactive Data Analysis (), pp.–, available from
http://stsdas.stsci.edu/perry/pydatatut.pdf (accessed ..); Brisson, Eric. Using IDL to Manipulate and Visualize Scientific Data, available from http://scv.bu.edu/Tutorials/IDL/ (accessed ..).
1
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
2.1
Arithmetic operators
Desc.
Assignment; defining a number
Addition
Subtraction
Multiplication
Division
Power, ab
IDL
a=1 & b=1
a + b
a - b
a * b
a / b
a ^ b
Remainder
a MOD b
Increment, return new value
Increment, return old value
In place operation to save array creation
overhead
Factorial, n!
++a or a+=1
a++
a+=1
2.2
a+=b or add(a,b,a)
rem(a,b)
Octave: ++a
Octave: a++
Octave: a+=1
factorial(a)
IDL
a eq
a lt
a gt
a le
a ge
a ne
b
b
b
b
b
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)
matlab/Octave
a == b
a < b
a > b
a <= b
a >= b
a ~= b
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
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
math.sqrt(a)
math.log(a)
math.log10(a)
math.log(a, 2)
math.exp(a)
matlab/Octave
sqrt(a)
log(a)
log10(a)
log2(a)
exp(a)
Logical operators
Desc.
Short-circuit logical AND
Short-circuit logical OR
Element-wise logical AND
Element-wise logical OR
Logical EXCLUSIVE OR
Logical NOT
IDL
a and b
a or b
a xor b
not a
True if any element is nonzero
True if all elements are nonzero
2.4
matlab/Octave
a=1; b=2;
a + b
a - b
a * b
a / b
a .^ b
Relational operators
Desc.
Equal
Less than
Greater than
Less than or equal
Greater than or equal
Not Equal
2.3
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)
root and logarithm
Desc.
Square root
Logarithm, base e (natural)
Logarithm, base 
Logarithm, base  (binary)
Exponential function
IDL
sqrt(a)
alog(a)
alog10(a)
exp(a)
√
a
ln a = loge a
log10 a
log2 a
ea
2
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
2.5
Round off
Desc.
Round
Round up
Round down
Round towards zero
2.6
Python
math.pi
math.e or math.exp(1)
matlab/Octave
pi
exp(1)
IDL
Python
nan
inf
plus_inf
minus_inf
plus_zero
minus_zero
matlab/Octave
NaN
Inf
IDL
complex(0,1)
z = complex(3,4)
abs(z)
real_part(z)
imaginary(z)
Python
z = 1j
z = 3+4j or z = complex(3,4)
abs(3+4j)
z.real
z.imag
conj(z)
z.conj(); z.conjugate()
matlab/Octave
i
z = 3+4i
abs(z)
real(z)
imag(z)
arg(z)
conj(z)
IDL
Python
atan2(b,a)
matlab/Octave
atan(a,b)
IDL
!pi
exp(1)
Complex numbers
Desc.
Imaginary unit
A complex number, 3 + 4i
Absolute value (modulus)
Real part
Imaginary part
Argument
Complex conjugate
2.8
matlab/Octave
round(a)
ceil(a)
floor(a)
fix(a)
Missing values; IEEE-754 floating point status flags
Desc.
Not a Number
Infinity, ∞
Infinity, +∞
Infinity, −∞
Plus zero, +0
Minus zero, −0
2.7
Python
around(a) or math.round(a)
ceil(a)
floor(a)
fix(a)
Mathematical constants
Desc.
π = 3.141592
e = 2.718281
2.6.1
IDL
round(a)
ceil(a)
floor(a)
√
−1
Trigonometry
Desc.
Arctangent, arctan(b/a)
Hypotenus; Euclidean distance
2.9
i=
p
hypot(x,y)
Generate random numbers
Desc.
Uniform distribution
IDL
randomu(seed, 10)
Python
random.random((10,))
random.uniform((10,))
matlab/Octave
rand(1,10)
Uniform: Numbers between  and 
2+5*randomu(seed, 10)
random.uniform(2,7,(10,))
2+5*rand(1,10)
Uniform: , array
randomu(seed,[6,6])
random.uniform(0,1,(6,6))
rand(6)
Normal distribution
randomn(seed, 10)
random.standard_normal((10,))
randn(1,10)
x2 + y 2
3
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
3
Vectors
Desc.
Row vector, 1 × n-matrix
Column vector, m × 1-matrix
3.1
.,.,., ... ,.
,,,
,,, ... ,
,,,
Linearly spaced vector of n= points
Reverse
Set all values to same scalar value
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
matlab/Octave
1:10
0:9
1:3:10
10:-1:1
10:-3:1
linspace(1,10,7)
reverse(a)
a(:) = 3
IDL
[a,a] or rebin(a,2,size(a))
[indgen(3)+1,a]
Python
concatenate((a,a))
concatenate((range(1,5),a), axis=1)
matlab/Octave
[a a]
[1:4 a]
IDL
Python
concatenate((a,a))
a.repeat(3) or
a.repeat(a) or
matlab/Octave
[a a]
Python
a[1:]
a[-1]
a[-2:]
matlab/Octave
a(2:end)
a([1:9])
a(end)
a(end-1:end)
Python
maximum(a,b)
concatenate((a,b)).max()
v,i = a.max(0),a.argmax(0)
matlab/Octave
max(a,b)
max([a b])
[v,i] = max(a)
reverse(a)
Miss those elements out
Desc.
miss the first element
miss the tenth element
last element
last two elements
3.5
IDL
indgen(10)+1
dindgen(10)+1
dindgen(10)
indgen(4)*3+1
Repeating
Desc.
  ,   
  ,   ,   
,  ,   
3.4
matlab/Octave
a=[2 3 4 5];
adash=[2 3 4 5]’;
Concatenation (vectors)
Desc.
Concatenate two vectors
3.3
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’]
Sequences
Desc.
,,, ... ,
3.2
IDL
a = [2, 3, 4, 5]
transpose([2,3,4,5])
IDL
Maximum and minimum
Desc.
pairwise max
max of all values in two vectors
IDL
4
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
3.6
Vector multiplication
Desc.
Multiply two vectors
Vector cross product, u × v
Vector dot product, u · v
4
IDL
Python
a*a
matlab/Octave
a.*a
dot(u,v)
dot(u,v)
crossp(u,v)
Matrices
Desc.
IDL
Python
matlab/Octave
Define a matrix
a = [[2,3],[4,5]]
a = array([[2,3],[4,5]])
a = [2 3;4 5]
4.1
2
4
3
5
i
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
Concatenation (matrices); rbind and cbind
Desc.
Bind rows
IDL
Python
matlab/Octave
concatenate((a,b), axis=0)
[a ; b]
vstack((a,b))
concatenate((a,b), axis=1)
[a , b]
hstack((a,b))
concatenate((a,b), axis=2)
dstack((a,b))
concatenate((a,b), axis=None)
[a(:), b(:)]
concatenate((r_[1:5],r_[1:5])).reshape(2,-1)
[1:4 ; 1:4]
vstack((r_[1:5],r_[1:5]))
[1:4 ; 1:4]’
Desc.
IDL
Python
matlab/Octave
 filled array
dblarr(3,5)
zeros((3,5),Float)
zeros(3,5)
 filled array of integers
intarr(3,5)
zeros((3,5))
 filled array
dblarr(3,5)+1
ones((3,5),Float)
Any number filled array
intarr(3,5)+9
Identity matrix
identity(3)
identity(3)
eye(3)
Diagonal
diag_matrix([4,5,6])
diag((4,5,6))
diag([4 5 6])
Bind columns
Bind slices (three-way arrays)
Concatenate matrices into one vector
Bind rows (from vectors)
Bind columns (from vectors)
4.2
h
Array creation
ones(3,5)
ones(3,5)*9
Magic squares; Lo Shu
Empty array
magic(3)
a = empty((3,3))
5
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
4.3
Reshape and flatten matrices
Desc.
IDL
Python
matlab/Octave
Reshaping (rows first)
reform(a,2,3)
arange(1,7).reshape(2,-1)
a.setshape(2,3)
reshape(1:6,3,2)’;
Reshaping (columns first)
arange(1,7).reshape(-1,2).transpose() reshape(1:6,2,3);
Flatten to vector (by rows, like comics)
a.flatten() or
a’(:)
Flatten to vector (by columns)
a.flatten(1)
a(:)
Flatten upper triangle (by columns)
4.4
1
4
2
5
3
6
i
h
1
2
3
4
5
6
i
1
2
3
4
5
6
1
4
2
5
3
6
vech(a)
IDL
Python
b = a.copy()
matlab/Octave
b = a
Indexing and accessing elements (Python: slicing)
Desc.
IDL
Python
matlab/Octave
Input is a , array
Element , (row,col)
First row
a = [[ 11, 12, 13, 14 ], $
[ 21, 22, 23, 24 ], $
[ 31, 32, 33, 34 ]]
a(2,1)
a(*,0)
a = array([[ 11, 12, 13, 14 ],
[ 21, 22, 23, 24 ],
[ 31, 32, 33, 34 ]])
a[1,2]
a[0,]
a = [ 11 12 13 14 ...
21 22 23 24 ...
31 32 33 34 ]
a(2,3)
a(1,:)
First column
a(0,*)
a[:,0]
a(:,1)
a.take([0,2]).take([0,3], axis=1)
a([1 3],[1 4]);
a[1:,]
a(2:end,:)
Last two rows
a[-2:,]
a(end-1:end,:)
Strides: Every other row
a[::2,:]
a(1:2:end,:)
Third in last dimension (axis)
a[...,2]
Array as indices
All, except first row
h
a(*,1:*)
h
h
Remove one column
a.take([0,2,3],axis=1)
Diagonal
a.diagonal(offset=0)
a(:,[1 3 4])
Assignment
Desc.
IDL
Clipping: Replace all elements over 
a>90
Clip upper and lower values
a < 2 > 5
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)
matlab/Octave
a(:,1) = 99
a(:,1) = [99 98 97]’
a(a>90) = 90;
a11
a21
a31
a
23
a11
a11
a21
h a31
a11
a31
4.6
Shared data (slicing)
Desc.
Copy of a
4.5
h
a12
a22
a32
a13
a23
a33
a14
a24
a34
a12
a13
a14
a24
a34
a24
a34
a14
a34
i
a14
a34
i
a21
a31
a21
a31
a11
a31
a22
a32
a22
a32
a12
a32
a23
a33
a23
a33
a13
a33
a11
a21
a31
a11
a13
a23
a33
a22
a14
a24
a34
a33
i
i
a44
6
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
4.7
Transpose and inverse
Desc.
Transpose
Python
a.conj().transpose()
matlab/Octave
a’
hqr(elmhes(a))
a.transpose()
linalg.det(a) or
linalg.inv(a) or
linalg.pinv(a)
norm(a)
linalg.eig(a)[0]
a.’ or transpose(a)
det(a)
inv(a)
pinv(a)
norm(a)
eig(a)
svdc,A,w,U,V
linalg.svd(a)
svd(a)
Cholesky factorization
Eigenvectors
linalg.cholesky(a)
linalg.eig(a)[1]
chol(a)
[v,l] = eig(a)
Rank
rank(a)
rank(a)
Python
a.sum(axis=0)
a.sum(axis=1)
a.sum()
a.trace(offset=0)
a.cumsum(axis=0)
matlab/Octave
sum(a)
sum(a’)
sum(sum(a))
cumsum(a)
Python
matlab/Octave
Non-conjugate transpose
Determinant
Inverse
Pseudo-inverse
Norms
Eigenvalues
Singular values
4.8
determ(a)
invert(a)
Sum
Desc.
Sum of each column
Sum of each row
Sum of all elements
Sum along diagonal
Cumulative sum (columns)
4.9
IDL
transpose(a)
IDL
total(a,2)
total(a,1)
total(a)
Sorting
Desc.
IDL
Example data
a = array([[4,3,2],[2,8,6],[1,4,7]]) a = [ 4 3 2 ; 2 8 6 ; 1 4 7 ]
Flat and sorted
a.ravel().sort() or
sort(a(:))
a.sort(axis=0) or msort(a)
sort(a)
Sort each row
a.sort(axis=1)
sort(a’)’
Sort rows (by first row)
a[a[:,0].argsort(),]
sortrows(a,1)
Sort, return indices
Sort each column, return indices
Sort each row, return indices
a.ravel().argsort()
a.argsort(axis=0)
a.argsort(axis=1)
Sort each column
sort(a)
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
7
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
4.10
Maximum and minimum
Desc.
max in each column
max in each row
max in array
return indices, i
pairwise max
IDL
max(a,DIMENSION=2)
max(a,DIMENSION=1)
max(a)
maximum(b,c)
max-to-min range
4.11
a.ptp(); a.ptp(0)
IDL
reverse(a)
reverse(a,2)
rotate(a,1)
Triangular, upper
Triangular, lower
Python
fliplr(a) or a[:,::-1]
flipud(a) or a[::-1,]
rot90(a)
kron(ones((2,3)),a)
triu(a)
tril(a)
matlab/Octave
fliplr(a)
flipud(a)
rot90(a)
repmat(a,2,3)
Octave: kron(ones(2,3),a)
triu(a)
tril(a)
Equivalents to ”size”
Desc.
Matrix dimensions
Number of columns
Number of elements
Number of dimensions
Number of bytes used in memory
4.13
matlab/Octave
max(a)
max(a’)
max(max(a))
[v i] = max(a)
max(b,c)
cummax(a)
Matrix manipulation
Desc.
Flip left-right
Flip up-down
Rotate  degrees
Repeat matrix: [ a a a ; a a a ]
4.12
Python
a.max(0) or amax(a [,axis=0])
a.max(1) or amax(a, axis=1)
a.max() or
IDL
size(a)
s=size(a) & s[1]
n_elements(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
matlab/Octave
size(a)
size(a,2) or length(a)
length(a(:))
ndims(a)
Matrix- and elementwise- multiplication
Desc.
IDL
Elementwise operations
Matrix product (dot product)
Inner matrix vector multiplication a · b0
a # b or b ## a
transpose(a) # b
Python
matlab/Octave
a * b or multiply(a,b)
a .* b
matrixmultiply(a,b)
a * b
h
1
9
h
7
15
5
11
1
2
3
4
1
3
3
9
h
inner(a,b) or
"
Outer product
a # b
outer(a,b) or
"
Kronecker product
Matrix division, b·a−1
Left matrix division, b−1 ·a
(solve linear equations)
Vector dot product
Cross product
cramer(a,b)
kron(a,b)
kron(a,b)
linalg.solve(a,b)
a / b
a \ b
vdot(a,b)
cross(a,b)
i
5
16
i
10
22
i
11
25
#
2
3
4
4
6
8
6
9 12
8 12 16
#
2
2
4
4
6
8
6
4
8
12 12 16
Ax = b
8
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
4.14
Find; conditional indexing
Desc.
Non-zero elements, indices
IDL
Python
a.ravel().nonzero()
matlab/Octave
find(a)
Non-zero elements, array indices
where(a NE 0)
(i,j) = a.nonzero()
(i,j) = where(a!=0)
[i j] = find(a)
Vector of non-zero values
a(where(a NE 0))
v = a.compress((a!=0).flat)
v = extract(a!=0,a)
[i j v] = find(a)
Condition, indices
where(a GE 5.5)
(a>5.5).nonzero()
find(a>5.5)
Return values
a(where(a GE 5.5))
a.compress((a>5.5).flat)
where(a>5.5,0,a) or a * (a>5.5)
a.put(2,indices)
Zero out elements above .
Replace values
5
Multi-way arrays
Desc.
Define a -way array
6
a .* (a>5.5)
IDL
Python
matlab/Octave
a = array([[[1,2],[1,2]], [[3,4],[3,4]]])
a = cat(3, [1 2; 1 2],[3 4; 3 4]);
a[0,...]
a(1,:,:)
File input and output
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)
IDL
read()
Python
matlab/Octave
f = fromfile("data.txt")
f = load(’data.txt’)
f = load("data.txt")
read()
f = load("data.txt")
f = load(’data.txt’)
x = read_ascii(data_start=1,delimiter=’;’)
f = load(’data.csv’, delimiter=’;’) x = dlmread(’data.csv’, ’;’)
save(’data.csv’, f, fmt=’%.6f’, delimiter=’;’)
save -ascii data.txt f
f.tofile(file=’data.csv’, format=’%.6f’, sep=’;’)
f = fromfile(file=’data.csv’, sep=’;’)
9
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
7
Plotting
7.1
Basic x-y plots
Desc.
IDL
Python
matlab/Octave
4
3
2
1
0
-1
-2
-3
-4
d line plot
plot, a
plot(a)
0
20
40
60
80
100
plot(a)
4.5
4.0
3.5
3.0
2.5
2.0
4.0
d scatter plot
plot, x(1,*), x(2,*)
plot(x[:,0],x[:,1],’o’)
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
plot(x(:,1),x(:,2),’o’)
7
6
5
4
3
2
1
4.0
Two graphs in one plot
Overplotting: Add new plots to current
subplots
Plotting symbols and color
7.1.1
plot, x1, y1
oplot, x2, y2
!p.multi(0,2,1)
plot, x,y, line=1, psym=-1
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, x2,y2)
plot(x1,y1)
hold on
plot(x2,y2)
subplot(211)
plot(x,y,’ro-’)
matlab/Octave
grid on
axis equal
Octave:
axis(’equal’)
replot
axis([ 0 10 0 5 ])
Axes and titles
Desc.
Turn on grid lines
: aspect ratio
IDL
Python
grid()
figure(figsize=(6,6))
Set axes manually
plot, x(1,*), x(2,*),
xran=[0,10], yran=[0,5]
plot, x,y, title=’title’,
xtitle=’x-axis’, ytitle=’y-axis’
axis([ 0, 10, 0, 5 ])
xyouts, 2,25, ’hello’
text(2,25,’hello’)
Axis labels and titles
Insert text
title(’title’)
xlabel(’x-axis’)
ylabel(’y-axis’)
10
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
7.1.2
Log plots
Desc.
logarithmic y-axis
logarithmic x-axis
logarithmic x and y axes
7.1.3
IDL
plot, x,y, /YLOG or plot_io, x,y
plot, x,y, /XLOG or plot_oi, x,y
plot_oo, x,y
Python
semilogy(a)
semilogx(a)
loglog(a)
matlab/Octave
semilogy(a)
semilogx(a)
loglog(a)
IDL
Python
matlab/Octave
fill(t,s,’b’, t,c,’g’, alpha=0.2)
fill(t,s,’b’, t,c,’g’)
Octave: % fill has a bug?
Python
matlab/Octave
f = inline(’sin(x/3) - cos(x/5)’)
Filled plots and bar plots
Desc.
Filled plot
7.1.4
Functions
IDL
x
3
f (x) = sin
●
●
●
●●
●●●
●
●
●
●
●
●
0.5
●
●
●
●●
●●●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●●
●●●●
●
●
●
●
f (x)
−0.5
●
●
●
●
●
●
●
●
●
●
●
●
●
●
−1.0
●
●
●
●
●
●
●
●
●
0.0
●
●
●
●
●
●
●
●
x
5
− cos
1.0
Desc.
Defining functions
●
●
●
●
●
●
●
●
●
−1.5
●
●
●
●
●
●
●
●
●
−2.0
●
0
Plot a function for given range
7.2
Desc.
x = arrayrange(0,40,.5)
y = sin(x/3) - cos(x/5)
plot(x,y, ’o’)
ezplot(f,[0,40])
fplot(’sin(x/3) - cos(x/5)’,[0,40])
Octave: % no ezplot
Python
theta = arange(0,2*pi,0.001)
r = sin(2*theta)
matlab/Octave
theta = 0:.001:2*pi;
r = sin(2*theta);
10
20
30
x
Polar plots
IDL
ρ(θ) = sin(2θ)
90
135
45
180
0
225
315
270
polar(theta, rho)
polar(theta, rho)
●●●●
●
40
11
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
Histogram plots
Desc.
7.4
7.4.1
IDL
plot, histogram(randomn(5,1000))
Python
matlab/Octave
hist(randn(1000,1))
hist(randn(1000,1), -4:4)
plot(sort(a))
IDL
Python
matlab/Octave
3d data
Contour and image plots
Desc.
0.0
2
6
0.
0.6
0.8
0.8
-0.6
-0.2
-0.4
0
0.2
1
0.4
7.3
1.0
-1
-0.2
-2
Contour plot
contour, z
-2
-1
0
1
2
-2
-1
0
1
2
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
contour, z, nlevels=7, /fill
contourf(Z, V,
contour, z, nlevels=7, /overplot, /downhill
cmap=cm.gray,
origin=’lower’,
extent=(-3,3,-3,3))
contourf(z); colormap(gray)
Plot image data
tv, z
loadct,0
image(z)
colormap(gray)
im = imshow(Z,
interpolation=’bilinear’,
origin=’lower’,
extent=(-3,3,-3,3))
0.0
2
6
0.
0.6
0.8
0.8
-0.6
-0.2
-0.4
0
0.2
1
0.4
Filled contour plot
1.0
-1
-0.2
-2
-2
Image with contours
Direction field vectors
# imshow() and contour() as above
quiver()
quiver()
-1
0
1
2
12
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
7.4.2
Perspective plots of surfaces over the x-y plane
Desc.
IDL
Python
matlab/Octave
n=arrayrange(-2,2,.1)
[x,y] = meshgrid(n,n)
z = x*power(math.e,-x**2-y**2)
n=-2:.1:2;
[x,y] = meshgrid(n,n);
z=x.*exp(-x.^2-y.^2);
2 −y 2
f (x, y) = xe−x
0.4
0.2
z
0.0
2
−0.2
1
−0.4
−2
y
0
−1
0
−1
x
1
2
Mesh plot
surface, z
−2
mesh(z)
0.4
0.2
z
0.0
2
−0.2
1
−0.4
−2
y
0
−1
0
−1
x
1
2
Surface plot
7.4.3
−2
surf(x,y,z) or surfl(x,y,z)
Octave: % no surfl()
shade_surf, z
loadct,3
Scatter (cloud) plots
Desc.
IDL
Python
matlab/Octave
’icc-gamut.csv’
80
60
40
20
0
-20
-40
-60
-80
100
90
80
70
60
80
50
60
40
40
20
30
0
20
-20
10
-40
d scatter plot
-60 0
plot3(x,y,z,’k+’)
13
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
7.5
Save plot to a graphics file
Desc.
PostScript
IDL
set_plot,’PS’
device, file=’foo.eps’, /land
plot x,y
device,/close & set_plot,’win’
PDF
SVG (vector graphics for www)
PNG (raster graphics)
8
8.1
Python
savefig(’foo.eps’)
savefig(’foo.pdf’)
savefig(’foo.svg’)
savefig(’foo.png’)
matlab/Octave
plot(1:10)
print -depsc2 foo.eps
Octave:
gset output "foo.eps"
gset terminal postscript eps
plot(1:10)
print -dpng foo.png
Data analysis
Set membership operators
Desc.
Create sets
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)
matlab/Octave
a = [ 1 2 2 5 2 ];
b = [ 2 3 4 ];
Set union
union1d(a,b)
a.union(b)
union(a,b)
Set intersection
intersect1d(a)
a.intersection(b)
intersect(a,b)
Set difference
setdiff1d(a,b)
a.difference(b)
setdiff(a,b)
Set exclusion
setxor1d(a,b)
a.symmetric_difference(b)
2 in a
setmember1d(2,a)
contains(a,2)
setxor(a,b)
Set unique
True for set member
IDL
unique(a)
ismember(2,a)
1
2
5
14
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
8.2
Statistics
Desc.
Average
IDL
mean(a)
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)
Median
Standard deviation
Variance
Correlation coefficient
Covariance
median(a)
stddev(a)
variance(a)
correlate(x,y)
median(a)
std(a)
var(a)
corr(x,y)
cov(x,y)
Linear least squares y = ax + b
Python
(a,b) = polyfit(x,y,1)
plot(x,y,’o’, x,a*x+b,’-’)
linalg.lstsq(x,y)
matlab/Octave
z = polyval(polyfit(x,y,1),x)
plot(x,y,’o’, x,z ,’-’)
a = x\y
Polynomial fit
polyfit(x,y,3)
polyfit(x,y,3)
Python
poly()
roots()
matlab/Octave
8.3
Interpolation and regression
Desc.
Straight line fit
8.4
8.4.1
IDL
poly_fit(x,y,1)
Non-linear methods
Polynomials, root finding
Desc.
Polynomial
Find zeros of polynomial
Find a zero near x = 1
IDL
roots([1 -1 -1])
f = inline(’1/x - (x-1)’)
fzero(f,1)
solve(’1/x = x-1’)
polyval(array([1,2,1,2]),arange(1,11))polyval([1 2 1 2],1:10)
Solve symbolic equations
Evaluate polynomial
8.4.2
Differential equations
Desc.
Discrete difference function and approximate derivative
Solve differential equations
8.5
IDL
Python
diff(x, n=1, axis=0)
matlab/Octave
diff(a)
IDL
fft(a)
fft(a),/inverse
convol()
Python
fft(a) or
ifft(a) or
convolve(x,y)
matlab/Octave
fft(a)
ifft(a)
Python
matlab/Octave
factor()
Fourier analysis
Desc.
Fast fourier transform
Inverse fourier transform
Linear convolution
9
matlab/Octave
mean(a)
Symbolic algebra; calculus
Desc.
Factorization
IDL
x2 − x − 1 = 0
1
− (x − 1)
f (x) = x
1
x
=x−1
15
MATLAB commands in numerical Python
Vidar Bronken Gundersen /mathesaurus.sf.net
10
Programming
Desc.
Script file extension
Comment symbol (rest of line)
IDL
.idlbatch
;
Python
.py
#
Import library functions
from pylab import *
Eval
string="a=234"
eval(string)
10.1
Loops
Desc.
for-statement
Multiline for statements
10.2
Python
for i in range(1,6): print(i)
for i in range(1,6):
print(i)
print(i*2)
matlab/Octave
for i=1:5; disp(i); end
for i=1:5
disp(i)
disp(i*2)
end
IDL
if 1 gt 0 then a=100
if 1 gt 0 then a=100 else a=0
a>0?a:0
Python
if 1>0: a=100
matlab/Octave
if 1>0 a=100; end
if 1>0 a=100; else a=0; end
IDL
Python
a > 0?a : 0
Debugging
Desc.
Most recent evaluated expression
List variables loaded into memory
Clear variable x from memory
Print
10.4
IDL
for k=1,5 do print,k
for k=1,5 do begin $
print, i &$
print, i*2 &$
end
Conditionals
Desc.
if-statement
if-else-statement
Ternary operator (if?true:false)
10.3
matlab/Octave
.m
%
Octave: % or #
% must be in MATLABPATH
Octave: % must be in LOADPATH
string=’a=234’;
eval(string)
print a
matlab/Octave
ans
whos or who
clear x or clear [all]
disp(a)
Python
os.listdir(".")
grep.grep("*.py")
os.getcwd()
os.chdir(’foo’)
os.system(’notepad’)
os.popen(’notepad’)
matlab/Octave
dir or ls
what
pwd
cd foo
!notepad
Octave: system("notepad")
help
print, a
Working directory and OS
Desc.
List files in directory
List script files in directory
Displays the current working directory
Change working directory
Invoke a System Command
IDL
dir
sd
cd,’foo or sd,’foo
spawn,’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/; Octave .., http://www.octave.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.
16