Introduction to NumPy (PyData SV 2013)

Introduction toIntroduction to
NumPyNumPy
Bryan Van de VenBryan Van de Ven

NumPy is a Python C extension library for array-oriented computing
Efficient
In-memory
Contiguous (or Strided)
Homogeneous (but types can be algebraic)
NumPy is suited to many applications
Image processing
Signal processing
Linear algebra
A plethora of others

NumPy is the foundation of theNumPy is the foundation of the
python scientific stackpython scientific stack

NumPy EcosystemNumPy Ecosystem

Quick StartQuick Start
In [1]: import numpy as np
In [2]: a = np.array([1,2,3,4,5,6,7,8,9])
In [3]: a
Out[3]: array([1, 2, 3, 4, 5, 6, 7, 8, 9])
In [4]: b = a.reshape((3,3))
In [5]: b
Out[5]:
array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
In [6]: b * 10 + 4
Out[6]:
array([[14, 24, 34],
[44, 54, 64],
[74, 84, 94]])

Array ShapeArray Shape
One dimensional arrays have a 1-tuple forOne dimensional arrays have a 1-tuple for
their shapetheir shape

...Two dimensional arrays have a 2-tuple...Two dimensional arrays have a 2-tuple

Array Element Type (dtype)Array Element Type (dtype)
NumPy arrays comprise elements of a single data type
The type object is accessible through the .dtype attribute
Here are a few of the most important attributes of dtype objects
dtype.byteorder — big or little endian
dtype.itemsize — element size of this dtype
dtype.name — a name for this dtype object
dtype.type — type object used to create scalars
There are many others...

Array dtypes are usually inferred automatically
But can also be specified explicitly
In [16]: a = np.array([1,2,3])
In [17]: a.dtype
Out[17]: dtype('int64')
In [18]: b = np.array([1,2,3,4.567])
In [19]: b.dtype
Out[19]: dtype('float64')
In [20]: a = np.array([1,2,3], dtype=np.float32)
In [21]: a.dtype
Out[21]: dtype('int64')
In [22]: a
Out[22]: array([ 1., 2., 3.], dtype=float32)

NumPy Builtin dtype HierarchyNumPy Builtin dtype Hierarchy
np.datetime64 is a new addition in NumPy 1.7

Array CreationArray Creation
Explicitly from a list of values
As a range of values
By specifying the number of elements
In [2]: np.array([1,2,3,4])
Out[2]: array([1, 2, 3, 4])
In [3]: np.arange(10)
Out[3]: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
In [4]: np.linspace(0, 1, 5)
Out[4]: array([ 0. , 0.25, 0.5 , 0.75, 1. ])

Zero-initialized
One-initialized
Uninitialized
In [4]: np.zeros((2,2))
Out[4]:
array([[ 0., 0.],
[ 0., 0.]])
In [5]: np.ones((1,5))
Out[5]: array([[ 1., 1., 1., 1., 1.]])
In [4]: np.empty((1,3))
Out[4]: array([[ 2.12716633e-314, 2.12716633e-314, 2.15203762e-314]])

Constant diagonal value
Multiple diagonal values
In [6]: np.eye(3)
Out[6]:
array([[ 1., 0., 0.],
[ 0., 1., 0.],
[ 0., 0., 1.]])
In [7]: np.diag([1,2,3,4])
Out[7]:
array([[1, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 3, 0],
[0, 0, 0, 4]])

Array Memory LayoutArray Memory Layout

Indexing and SlicingIndexing and Slicing

Introduction to NumPy (PyData SV 2013)

NumPy array indices can also take an optional stride

Array ViewsArray Views
Simple assigments do not make copies of arrays (same semantics as
Python). Slicing operations do not make copies either; they return views
on the original array.
Array views contain a pointer to the original data, but may have different
shape or stride values. Views always have flags.owndata equal to
False.
In [2]: a = np.arange(10)
In [3]: b = a[3:7]
In [4]: b
Out[4]: array([3, 4, 5, 6])
In [5]: b[:] = 0
In [6]: a
Out[6]: array([0, 1, 3, 0, 0, 0, 0, 7, 8, 9])
In [7]: b.flags.owndata
Out[7]: False

Universal Functions (ufuncs)Universal Functions (ufuncs)
NumPy ufuncs are functions that operate element-wise on one or more
arrays
ufuncs dispatch to optimized C inner-loops based on array dtype

NumPy has many built-in ufuncsNumPy has many built-in ufuncs
comparison: <, <=, ==, !=, >=, >
arithmetic: +, -, *, /, reciprocal, square
exponential: exp, expm1, exp2, log, log10, log1p, log2,
power, sqrt
trigonometric: sin, cos, tan, acsin, arccos, atctan
hyperbolic: sinh, cosh, tanh, acsinh, arccosh, atctanh
bitwise operations: &, |, ~, ^, left_shift, right_shift
logical operations: and, logical_xor, not, or
predicates: isfinite, isinf, isnan, signbit
other: abs, ceil, floor, mod, modf, round, sinc, sign,
trunc

AxisAxis
Array method reductions take an optional axis parameter that specifies
over which axes to reduce
axis=None reduces into a single scalar
In [7]: a.sum
()
Out[7]: 105

axis=0 reduces into the zeroth dimension
axis=0 reduces into the first dimension
In [8]: a.sum(axis=0)
Out[8]: array([15, 18, 21, 24,
27])
In [9]: a.sum(axis=1)
Out[9]: array([10, 35, 60])

BroadcastingBroadcasting
A key feature of NumPy is broadcasting, where arrays with different, but
compatible shapes can be used as arguments to ufuncs
In this case an array scalar is broadcast to an array with shape (5, )

A slightly more involved broadcasting example in two dimensions
Here an array of shape (3, 1) is broadcast to an array with shape
(3, 2)

Broadcasting RulesBroadcasting Rules
In order for an operation to broadcast, the size of all the trailing
dimensions for both arrays must either:
be equal OR be one
A (1d array): 3
B (2d array): 2 x 3
Result (2d array): 2 x 3
A (2d array): 6 x 1
B (3d array): 1 x 6 x 4
Result (3d array): 1 x 6 x 4
A (4d array): 3 x 1 x 6 x 1
B (3d array): 2 x 1 x 4
Result (4d array): 3 x 2 x 6 x 4

Square Peg in a Round HoleSquare Peg in a Round Hole
If the dimensions do not match up, np.newaxis may be useful
In [16]: a = np.arange(6).reshape((2, 3))
In [17]: b = np.array([10, 100])
In [18]: a * b
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
in ()
----> 1 a * b
ValueError: operands could not be broadcast together with shapes (2,3) (2)
In [19]: b[:,np.newaxis].shape
Out[19]: (2, 1)
In [20]: a *b[:,np.newaxis]
Out[20]:
array([[ 0, 10, 20],
[300, 400, 500]])

Array MethodsArray Methods
Predicates
a.any(), a.all()
Reductions
a.mean(), a.argmin(), a.argmax(), a.trace(),
a.cumsum(), a.cumprod()
Manipulation
a.argsort(), a.transpose(), a.reshape(...),
a.ravel(), a.fill(...), a.clip(...)
Complex Numbers
a.real, a.imag, a.conj()

Fancy IndexingFancy Indexing
NumPy arrays may be used to index into other arrays
In [2]: a = np.arange(15).reshape((3,5))
In [3]: a
Out[3]:
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
In [4]: i = np.array([[0,1], [1, 2]])
In [5]: j = np.array([[2, 1], [4, 4]])
In [6]: a[i,j]
Out[6]:
array([[ 2, 6],
[ 9, 14]])

Boolean arrays can also be used as indices into other arrays
In [2]: a = np.arange(15).reshape((3,5))
In [3]: a
Out[3]:
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
In [4]: b = (a % 3 == 0)
In [5]: b
Out[5]:
array([[ True, False, False, True, False],
[False, True, False, False, True],
[False, False, True, False, False]], dtype=bool)
In [6]: a[b]
Out[6]: array([ 0, 3, 6, 9, 12])

NumPy FunctionsNumPy Functions
Data I/O
fromfile, genfromtxt, load, loadtxt, save, savetxt
Mesh Creation
mgrid, meshgrid, ogrid
Manipulation
einsum, hstack, take, vstack

Array SubclassesArray Subclasses
numpy.ma — Masked arrays
numpy.matrix — Matrix operators
numpy.memmap — Memory-mapped arrays
numpy.recarray — Record arrays

Other SubpackagesOther Subpackages
numpy.fft — Fast Fourier transforms
numpy.polynomial — Efficient polynomials
numpy.linalg — Linear algebra
cholesky, det, eig, eigvals, inv, lstsq, norm, qr,
svd
numpy.math — C standard library math functions
numpy.random — Random number generation
beta, gamma, geometric, hypergeometric, lognormal,
normal, poisson, uniform, weibull

FFTFFT
import numpy as np
t = np.linspace(0,120,4000)
PI = np.pi
signal = 12*np.sin(3 * 2*PI*t) # 3 Hz
signal += 6*np.sin(8 * 2*PI*t) # 8 Hz
signal += 1.5*np.random.random(len(t)) # noise
FFT = abs(np.fft.fft(signal))
freqs = np.fft.fftfreq(signal.size, t[1]-t[0])

ResourcesResources
These slides are currently available at
http://docs.scipy.org/doc/numpy/reference/
http://docs.scipy.org/doc/numpy/user/index.html
http://www.scipy.org/Tentative_NumPy_Tutorial
http://www.scipy.org/Numpy_Example_List
https://github.com/ContinuumIO/tutorials/blob/master/IntrotoNumPy.pdf

The EndThe End
Many thanks toMany thanks to
Ben Zaitlin
Stéfan van der Walt
Amy Troschinetz
Maggie Mari
Travis Oliphant
Questions?Questions?

Introduction to NumPy (PyData SV 2013)

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