NumPy for Numeric/numarray users

Help

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`help()`	Browse help interactively
	`help`	Help on using help
	`help(plot)` or `?plot`	Help for a function
	`help(pylab)`	Help for a toolbox/library package

Searching available documentation

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`help(); modules [Numeric]`	List available packages
	`help(plot)`	Locate functions

Using interactively

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`ipython -pylab`	Start session
	`TAB`	Auto completion
	`execfile('foo.py')` or `run foo.py`	Run code from file
	`hist -n`	Command history
	`CTRL-D` `CTRL-Z # windows` `sys.exit()`	End session

Operators

Numeric (typical differences)	Python; NumPy, Matplotlib	Description

Arithmetic operators

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a=1; b=1`	Assignment; defining a number
	`a + b` or `add(a,b)`	Addition
	`a - b` or `subtract(a,b)`	Subtraction
	`a * b` or `multiply(a,b)`	Multiplication
	`a / b` or `divide(a,b)`	Division
	`a ** b` `power(a,b)` `pow(a,b)`	Power, $a^b$
	`a % b` `remainder(a,b)` `fmod(a,b)`	Remainder
	`a+=b` or `add(a,b,a)`	In place operation to save array creation overhead

Relational operators

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a == b` or `equal(a,b)`	Equal
	`a < b` or `less(a,b)`	Less than
	`a > b` or `greater(a,b)`	Greater than
	`a <= b` or `less_equal(a,b)`	Less than or equal
	`a >= b` or `greater_equal(a,b)`	Greater than or equal
	`a != b` or `not_equal(a,b)`	Not Equal

Logical operators

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a and b`	Short-circuit logical AND
	`a or b`	Short-circuit logical OR
	`logical_and(a,b)` or `a and b`	Element-wise logical AND
	`logical_or(a,b)` or `a or b`	Element-wise logical OR
	`logical_xor(a,b)`	Logical EXCLUSIVE OR
	`logical_not(a)` or `not a`	Logical NOT

root and logarithm

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`math.sqrt(a)`	Square root
	`math.log(a)`	Logarithm, base $e$ (natural)
	`math.log10(a)`	Logarithm, base 10
	`math.log(a, 2)`	Logarithm, base 2 (binary)
	`math.exp(a)`	Exponential function

Round off

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`around(a)` or `math.round(a)`	Round
	`ceil(a)`	Round up
	`floor(a)`	Round down
	`fix(a)`	Round towards zero

Mathematical constants

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`math.pi`	$\pi=3.141592$
	`math.e` or `math.exp(1)`	$e=2.718281$

Missing values; IEEE-754 floating point status flags

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`nan`	Not a Number
	`inf`	Infinity, $\infty$
	`plus_inf`	Infinity, $+\infty$
	`minus_inf`	Infinity, $-\infty$
	`plus_zero`	Plus zero, $+0$
	`minus_zero`	Minus zero, $-0$

Complex numbers

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`z = 1j`	Imaginary unit
	`z = 3+4j` or `z = complex(3,4)`	A complex number, $3+4i$
	`abs(3+4j)`	Absolute value (modulus)
	`z.real`	Real part
	`z.imag`	Imaginary part
	`z.conj(); z.conjugate()`	Complex conjugate

Trigonometry

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`atan2(b,a)`	Arctangent, $\arctan(b/a)$
	`hypot(x,y)`	Hypotenus; Euclidean distance

Generate random numbers

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
`random((10,))` `uniform(0,1,(10,))`	`random.random((10,))` `random.uniform((10,))`	Uniform distribution
`uniform(2,7,(10,))`	`random.uniform(2,7,(10,))`	Uniform: Numbers between 2 and 7
`uniform(0,1,(6,6))`	`random.uniform(0,1,(6,6))`	Uniform: 6,6 array
`standard_normal((10,))`	`random.standard_normal((10,))`	Normal distribution

Vectors

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a=array([2,3,4,5])`	Row vector, $1 \times n$-matrix
`transpose(array([2,3,4,5]))`	`array([2,3,4,5])[:,NewAxis]` `array([2,3,4,5]).reshape(-1,1)` `r_[1:10,'c']`	Column vector, $m \times 1$-matrix

Sequences

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
`arange(1,11, typecode=Float)`	`arange(1,11, dtype=Float)` `range(1,11)`	1,2,3, ... ,10
	`arange(10.)`	0.0,1.0,2.0, ... ,9.0
	`arange(1,11,3)`	1,4,7,10
	`arange(10,0,-1)`	10,9,8, ... ,1
	`arange(10,0,-3)`	10,7,4,1
	`linspace(1,10,7)`	Linearly spaced vector of n=7 points
`a[::-1]; a.reverse()`	`a[::-1]`	Reverse
	`a.fill(3), a[:] = 3`	Set all values to same scalar value

Concatenation (vectors)

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`concatenate((a,a))`	Concatenate two vectors
	`concatenate((range(1,5),a), axis=1)`

Repeating

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`concatenate((a,a))`	1 2 3, 1 2 3
`repeat(a,3)`	`a.repeat(3)`	1 1 1, 2 2 2, 3 3 3
`repeat(a,a)`	`a.repeat(a)`	1, 2 2, 3 3 3

Miss those elements out

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a[1:]`	miss the first element
	`a[-1]`	last element
	`a[-2:]`	last two elements

Maximum and minimum

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`maximum(a,b)`	pairwise max
	`concatenate((a,b)).max()`	max of all values in two vectors
	`v,i = a.max(0),a.argmax(0)`

Vector multiplication

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a*a`	Multiply two vectors
	`dot(u,v)`	Vector dot product, $u \cdot v$

Matrices

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a = array([[2,3],[4,5]])`	Define a matrix

Concatenation (matrices); rbind and cbind

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`concatenate((a,b), axis=0)` `vstack((a,b))`	Bind rows
	`concatenate((a,b), axis=1)` `hstack((a,b))`	Bind columns
	`concatenate((a,b), axis=2)` `dstack((a,b))`	Bind slices (three-way arrays)
	`concatenate((a,b), axis=None)`	Concatenate matrices into one vector
	`concatenate((r_[1:5],r_[1:5])).reshape(2,-1)` `vstack((r_[1:5],r_[1:5]))`	Bind rows (from vectors)

Array creation

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`zeros((3,5),Float)`	0 filled array
	`zeros((3,5))`	0 filled array of integers
	`ones((3,5),Float)`	1 filled array
`ones((3,5))*9`		Any number filled array
	`identity(3)`	Identity matrix
	`diag((4,5,6))`	Diagonal
	`a = empty((3,3))`	Empty array

Reshape and flatten matrices

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
`a.shape = (2,3)`	`arange(1,7).reshape(2,-1)` `a.setshape(2,3)`	Reshaping (rows first)
	`arange(1,7).reshape(-1,2).transpose()`	Reshaping (columns first)
`ravel(a)`	`a.flatten()`	Flatten to vector (by rows, like comics)
`ravel(transpose(a))`	`a.flatten(1)`	Flatten to vector (by columns)

Shared data (slicing)

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`b = a.copy()`	Copy of a

Indexing and accessing elements (Python: slicing)

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a = array([[ 11, 12, 13, 14 ],` `[ 21, 22, 23, 24 ],` `[ 31, 32, 33, 34 ]])`	Input is a 3,4 array
	`a[1,2]`	Element 2,3 (row,col)
	`a[0,]`	First row
	`a[:,0]`	First column
`take(take(a,[0,2]),[0,3], axis=1)`	`a.take([0,2]).take([0,3], axis=1)`	Array as indices
	`a[1:,]`	All, except first row
	`a[-2:,]`	Last two rows
	`a[::2,:]`	Strides: Every other row
	`a[...,2]`	Third in last dimension (axis)
`take(a,[0,2,3],axis=1)`	`a.take([0,2,3],axis=1)`	Remove one column
	`a.diagonal(offset=0)`	Diagonal

Assignment

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a[:,0] = 99`
	`a[:,0] = array([99,98,97])`
`choose(a>90, (a,90))`	`(a>90).choose(a,90)` `a.clip(min=None, max=90)`	Clipping: Replace all elements over 90
`clip(a,2,5)`	`a.clip(min=2, max=5)`	Clip upper and lower values

Transpose and inverse

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
`transpose(a)`	`a.conj().transpose()`	Transpose
	`a.transpose()`	Non-conjugate transpose
`determinant(a)`	`linalg.det(a)`	Determinant
`inverse(a)`	`linalg.inv(a)`	Inverse
	`linalg.pinv(a)`	Pseudo-inverse
	`norm(a)`	Norms
`eigenvalues(a)`	`linalg.eig(a)[0]`	Eigenvalues
`singular_value_decomposition(a)`	`linalg.svd(a)`	Singular values
	`linalg.cholesky(a)`	Cholesky factorization
`eigenvectors(a)`	`linalg.eig(a)[1]`	Eigenvectors
	`rank(a)`	Rank

Sum

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a.sum(axis=0)`	Sum of each column
	`a.sum(axis=1)`	Sum of each row
	`a.sum()`	Sum of all elements
	`a.trace(offset=0)`	Sum along diagonal
	`a.cumsum(axis=0)`	Cumulative sum (columns)

Sorting

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a = array([[4,3,2],[2,8,6],[1,4,7]])`	Example data
`sort(a.flat)`	`a.ravel().sort()`	Flat and sorted
	`a.sort(axis=0)` or `msort(a)`	Sort each column
	`a.sort(axis=1)`	Sort each row
	`a[a[:,0].argsort(),]`	Sort rows (by first row)
	`a.ravel().argsort()`	Sort, return indices
	`a.argsort(axis=0)`	Sort each column, return indices
	`a.argsort(axis=1)`	Sort each row, return indices

Maximum and minimum

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a.max(0)` or `amax(a [,axis=0])`	max in each column
	`a.max(1)` or `amax(a, axis=1)`	max in each row
`max(a.flat)`	`a.max()`	max in array
	`maximum(b,c)`	pairwise max
	`a.ptp(); a.ptp(0)`	max-to-min range

Matrix manipulation

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`fliplr(a)` or `a[:,::-1]`	Flip left-right
	`flipud(a)` or `a[::-1,]`	Flip up-down
	`rot90(a)`	Rotate 90 degrees
	`kron(ones((2,3)),a)`	Repeat matrix: [ a a a ; a a a ]
	`triu(a)`	Triangular, upper
	`tril(a)`	Triangular, lower

Equivalents to "size"

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
`a.shape`	`a.shape` or `a.getshape()`	Matrix dimensions
`a.shape[1]` or `size(a, axis=1)`	`a.shape[1]` or `size(a, axis=1)`	Number of columns
	`a.size` or `size(a[, axis=None])`	Number of elements
	`a.ndim`	Number of dimensions
	`a.nbytes`	Number of bytes used in memory

Matrix- and elementwise- multiplication

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a * b` or `multiply(a,b)`	Elementwise operations
	`matrixmultiply(a,b)`	Matrix product (dot product)
`innerproduct(a,b)`	`inner(a,b)`	Inner matrix vector multiplication $a\cdot b'$
`outerproduct(a,b)`	`outer(a,b)`	Outer product
	`kron(a,b)`	Kronecker product
`solve_linear_equations(a,b)`	`linalg.solve(a,b)`	Left matrix division, $b^{-1}{\cdot}a$ \newline (solve linear equations)
	`vdot(a,b)`	Vector dot product
	`cross(a,b)`	Cross product

Find; conditional indexing

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
`nonzero(a.flat)`	`a.ravel().nonzero()`	Non-zero elements, indices
`(i,j) = nonzero(a)`	`(i,j) = a.nonzero()` `(i,j) = where(a!=0)`	Non-zero elements, array indices
`v = compress(a.flat!=0, a.flat)`	`v = a.compress((a!=0).flat)` `v = extract(a!=0,a)`	Vector of non-zero values
`nonzero(a.flat>5.5)`	`(a>5.5).nonzero()`	Condition, indices
`compress(a.flat>5.5, a.flat)`	`a.compress((a>5.5).flat)`	Return values
	`where(a>5.5,0,a)` or `a * (a>5.5)`	Zero out elements above 5.5
	`a.put(2,indices)`	Replace values

Multi-way arrays

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a = array([[[1,2],[1,2]], [[3,4],[3,4]]])`	Define a 3-way array
	`a[0,...]`

File input and output

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`f = fromfile("data.txt")` `f = load("data.txt")`	Reading from a file (2d)
	`f = load("data.txt")`	Reading from a file (2d)
	`f = load('data.csv', delimiter=';')`	Reading fram a CSV file (2d)
	`save('data.csv', f, fmt='%.6f', delimiter=';')`	Writing to a file (2d)
	`f.tofile(file='data.csv', format='%.6f', sep=';')`	Writing to a file (1d)
	`f = fromfile(file='data.csv', sep=';')`	Reading from a file (1d)

Plotting

Basic x-y plots

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`plot(a)`	1d line plot
	`plot(x[:,0],x[:,1],'o')`	2d scatter plot
	`plot(x1,y1,'bo', x2,y2,'go')`	Two graphs in one plot
	`plot(x1,y1,'o')` `plot(x2,y2,'o')` `show() # as normal`	Overplotting: Add new plots to current
	`subplot(211)`	subplots
	`plot(x,y,'ro-')`	Plotting symbols and color

Axes and titles

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`grid()`	Turn on grid lines
	`figure(figsize=(6,6))`	1:1 aspect ratio
	`axis([ 0, 10, 0, 5 ])`	Set axes manually
	`text(2,25,'hello')`	Insert text

Log plots

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`semilogy(a)`	logarithmic y-axis
	`semilogx(a)`	logarithmic x-axis
	`loglog(a)`	logarithmic x and y axes

Filled plots and bar plots

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`fill(t,s,'b', t,c,'g', alpha=0.2)`	Filled plot

Functions

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`x = arrayrange(0,40,.5)` `y = sin(x/3) - cos(x/5)` `plot(x,y, 'o')`	Plot a function for given range

Polar plots

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`theta = arange(0,2pi,0.001)` `r = sin(2theta)`
	`polar(theta, rho)`

Histogram plots

Numeric (typical differences)	Python; NumPy, Matplotlib	Description

3d data

Contour and image plots

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`levels, colls = contour(Z, V,` `origin='lower', extent=(-3,3,-3,3))` `clabel(colls, levels, inline=1,` `fmt='%1.1f', fontsize=10)`	Contour plot
	`contourf(Z, V,` `cmap=cm.gray,` `origin='lower',` `extent=(-3,3,-3,3))`	Filled contour plot
	`im = imshow(Z,` `interpolation='bilinear',` `origin='lower',` `extent=(-3,3,-3,3))`	Plot image data
	`# imshow() and contour() as above`	Image with contours
	`quiver()`	Direction field vectors

Perspective plots of surfaces over the x-y plane

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`n=arrayrange(-2,2,.1)` `[x,y] = meshgrid(n,n)` `z = xpower(math.e,-x2-y*2)`
		Mesh plot

Scatter (cloud) plots

Numeric (typical differences)	Python; NumPy, Matplotlib	Description

Save plot to a graphics file

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`savefig('foo.eps')`	PostScript
	`savefig('foo.pdf')`	PDF
	`savefig('foo.svg')`	SVG (vector graphics for www)
	`savefig('foo.png')`	PNG (raster graphics)

Data analysis

Set membership operators

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`a = array([1,2,2,5,2])` `b = array([2,3,4])` `a = set([1,2,2,5,2])` `b = set([2,3,4])`	Create sets
	`unique1d(a)` `unique(a)` `set(a)`	Set unique
	`union1d(a,b)` `a.union(b)`	Set union
	`intersect1d(a)` `a.intersection(b)`	Set intersection
	`setdiff1d(a,b)` `a.difference(b)`	Set difference
	`setxor1d(a,b)` `a.symmetric_difference(b)`	Set exclusion
	`2 in a` `setmember1d(2,a)` `contains(a,2)`	True for set member

Statistics

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
`average(a [,axis=0])`	`a.mean(axis=0)` `mean(a [,axis=0])`	Average
	`median(a)` or `median(a [,axis=0])`	Median
	`a.std(axis=0)` or `std(a [,axis=0])`	Standard deviation
	`a.var(axis=0)` or `var(a)`	Variance
	`correlate(x,y)` or `corrcoef(x,y)`	Correlation coefficient
	`cov(x,y)`	Covariance

Interpolation and regression

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`(a,b) = polyfit(x,y,1)` `plot(x,y,'o', x,a*x+b,'-')`	Straight line fit
`(a,b) = linear_least_squares(x,y)[0]`	`linalg.lstsq(x,y)`	Linear least squares $y = ax + b$
	`polyfit(x,y,3)`	Polynomial fit

Non-linear methods

Polynomials, root finding

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`poly()`	Polynomial
	`roots()`	Find zeros of polynomial
	`polyval(array([1,2,1,2]),arange(1,11))`	Evaluate polynomial

Differential equations

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`diff(x, n=1, axis=0)`	Discrete difference function and approximate derivative

Fourier analysis

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
`fft(a)`	`fft(a)`	Fast fourier transform
`inverse_fft(a)`	`ifft(a)`	Inverse fourier transform
	`convolve(x,y)`	Linear convolution

Symbolic algebra; calculus

Numeric (typical differences)	Python; NumPy, Matplotlib	Description

Programming

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`.py`	Script file extension
	`#`	Comment symbol (rest of line)
	`from pylab import *`	Import library functions
	`string="a=234"` `eval(string)`	Eval

Loops

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`for i in range(1,6): print(i)`	for-statement
	`for i in range(1,6):` `print(i)` `print(i*2)`	Multiline for statements

Conditionals

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`if 1>0: a=100`	if-statement

Debugging

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`print a`	Print

Working directory and OS

Numeric (typical differences)	Python; NumPy, Matplotlib	Description
	`os.listdir(".")`	List files in directory
	`grep.grep("*.py")`	List script files in directory
	`os.getcwd()`	Displays the current working directory
	`os.chdir('foo')`	Change working directory
	`os.system('notepad')` `os.popen('notepad')`	Invoke a System Command

Time-stamp: "2007-11-09T16:46:36 vidar"
©2006 Vidar Bronken Gundersen, /mathesaurus.sf.net
Permission is granted to copy, distribute and/or modify this document as long as the above attribution is retained.