![NumPy
11
The above constructor takes the following parameters:
object
Any object exposing the array interface method returns an array, or any
(nested) sequence
dtype Desired data type of array, optional
copy Optional. By default (true), the object is copied
order C (row major) or F (column major) or A (any) (default)
subok
By default, returned array forced to be a base class array. If true, sub-classes
passed through
ndimin Specifies minimum dimensions of resultant array
Take a look at the following examples to understand better.
Example 1
import numpy as np
a=np.array([1,2,3])
print a
The output is as follows:
[1, 2, 3]
Example 2
# more than one dimensions
import numpy as np](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-12-320.jpg)
![NumPy
12
a = np.array([[1, 2], [3, 4]])
print a
The output is as follows:
[[1, 2]
[3, 4]]
Example 3
# minimum dimensions
import numpy as np
a=np.array([1, 2, 3,4,5], ndmin=2)
print a
The output is as follows:
[[1, 2, 3, 4, 5]]
Example 4
# dtype parameter
import numpy as np
a = np.array([1, 2, 3], dtype=complex)
print a
The output is as follows:
[ 1.+0.j, 2.+0.j, 3.+0.j]
The ndarray object consists of contiguous one-dimensional segment of computer memory,
combined with an indexing scheme that maps each item to a location in the memory block.
The memory block holds the elements in a row-major order (C style) or a column-major order
(FORTRAN or MatLab style).](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-13-320.jpg)
![NumPy
15
Example 2
#int8, int16, int32, int64 can be replaced by equivalent string 'i1', 'i2','i4',
etc.
import numpy as np
dt = np.dtype('i4')
print dt
The output is as follows:
int32
Example 3
# using endian notation
import numpy as np
dt = np.dtype('>i4')
print dt
The output is as follows:
>i4
The following examples show the use of structured data type. Here, the field name and the
corresponding scalar data type is to be declared.
Example 4
# first create structured data type
import numpy as np
dt = np.dtype([('age',np.int8)])
print dt
The output is as follows:
[('age', 'i1')]
Example 5
# now apply it to ndarray object](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-16-320.jpg)
![NumPy
16
import numpy as np
dt = np.dtype([('age',np.int8)])
a = np.array([(10,),(20,),(30,)], dtype=dt)
print a
The output is as follows:
[(10,) (20,) (30,)]
Example 6
# file name can be used to access content of age column
import numpy as np
dt = np.dtype([('age',np.int8)])
a = np.array([(10,),(20,),(30,)], dtype=dt)
print a['age']
The output is as follows:
[10 20 30]
Example 7
The following examples define a structured data type called student with a string field 'name',
an integer field 'age' and a float field 'marks'. This dtype is applied to ndarray object.
import numpy as np
student=np.dtype([('name','S20'), ('age', 'i1'), ('marks', 'f4')])
print student
The output is as follows:
[('name', 'S20'), ('age', 'i1'), ('marks', '<f4')])
Example 8
import numpy as np
student=np.dtype([('name','S20'), ('age', 'i1'), ('marks', 'f4')])
a = np.array([('abc', 21, 50),('xyz', 18, 75)], dtype=student)](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-17-320.jpg)
![NumPy
17
print a
The output is as follows:
[('abc', 21, 50.0), ('xyz', 18, 75.0)]
Each built-in data type has a character code that uniquely identifies it.
'b': boolean
'i': (signed) integer
'u': unsigned integer
'f': floating-point
'c': complex-floating point
'm': timedelta
'M': datetime
'O': (Python) objects
'S', 'a': (byte-)string
'U': Unicode
'V': raw data (void)](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-18-320.jpg)
![NumPy
18
In this chapter, we will discuss the various array attributes of NumPy.
ndarray.shape
This array attribute returns a tuple consisting of array dimensions. It can also be used to
resize the array.
Example 1
import numpy as np
a=np.array([[1,2,3],[4,5,6]])
print a.shape
The output is as follows:
(2, 3)
Example 2
# this resizes the ndarray
import numpy as np
a=np.array([[1,2,3],[4,5,6]])
a.shape=(3,2)
print a
The output is as follows:
[[1 2]
[3 4]
[5 6]]
Example 3
NumPy also provides a reshape function to resize an array.
import numpy as np
5. NUMPY − ARRAY ATTRIBUTES](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-19-320.jpg)
![NumPy
19
a = np.array([[1,2,3],[4,5,6]])
b = a.reshape(3,2)
print b
The output is as follows:
[[1 2]
[3 4]
[5 6]]
ndarray.ndim
This array attribute returns the number of array dimensions.
Example 4
# an array of evenly spaced numbers
import numpy as np
a = np.arange(24)
print a
The output is as follows:
[0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23]
Example 5
# this is one dimensional array
import numpy as np
a = np.arange(24)
a.ndim
# now reshape it
b = a.reshape(2,4,3)
print b
# b is having three dimensions
The output is as follows:](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-20-320.jpg)
![NumPy
20
[[[ 0, 1, 2]
[ 3, 4, 5]
[ 6, 7, 8]
[ 9, 10, 11]]
[[12, 13, 14]
[15, 16, 17]
[18, 19, 20]
[21, 22, 23]]]
numpy.itemsize
This array attribute returns the length of each element of array in bytes.
Example 6
# dtype of array is int8 (1 byte)
import numpy as np
x = np.array([1,2,3,4,5], dtype=np.int8)
print x.itemsize
The output is as follows:
1
Example 7
# dtype of array is now float32 (4 bytes)
import numpy as np
x = np.array([1,2,3,4,5], dtype=np.float32)
print x.itemsize
The output is as follows:
4](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-21-320.jpg)
![NumPy
21
numpy.flags
The ndarray object has the following attributes. Its current values are returned by this
function.
C_CONTIGUOUS (C) The data is in a single, C-style contiguous segment
F_CONTIGUOUS (F) The data is in a single, Fortran-style contiguous segment
OWNDATA (O) The array owns the memory it uses or borrows it from another object
WRITEABLE (W) The data area can be written to. Setting this to False locks the data,
making it read-only
ALIGNED (A) The data and all elements are aligned appropriately for the hardware
UPDATEIFCOPY (U)
This array is a copy of some other array. When this array is
deallocated, the base array will be updated with the contents of this
array
Example 8
The following example shows the current values of flags.
import numpy as np
x = np.array([1,2,3,4,5])
print x.flags
The output is as follows:
C_CONTIGUOUS : True
F_CONTIGUOUS : True
OWNDATA : True
WRITEABLE : True
ALIGNED : True
UPDATEIFCOPY : False](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-22-320.jpg)
![NumPy
22
A new ndarray object can be constructed by any of the following array creation routines or
using a low-level ndarray constructor.
numpy.empty
It creates an uninitialized array of specified shape and dtype. It uses the following constructor:
numpy.empty(shape, dtype=float, order='C')
The constructor takes the following parameters.
Shape Shape of an empty array in int or tuple of int
Dtype Desired output data type. Optional
Order 'C' for C-style row-major array, 'F' for FORTRAN style column-major array
Example 1
The following code shows an example of an empty array.
import numpy as np
x = np.empty([3,2], dtype=int)
print x
The output is as follows:
[[22649312 1701344351]
[1818321759 1885959276]
[16779776 156368896]]
Note: The elements in an array show random values as they are not initialized.
6. NUMPY − ARRAY CREATION ROUTINES](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-23-320.jpg)
![NumPy
23
numpy.zeros
Returns a new array of specified size, filled with zeros.
numpy.zeros(shape, dtype=float, order='C')
The constructor takes the following parameters.
Shape Shape of an empty array in int or sequence of int
Dtype Desired output data type. Optional
Order 'C' for C-style row-major array, 'F' for FORTRAN style column-major array
Example 2
# array of five zeros. Default dtype is float
import numpy as np
x = np.zeros(5)
print x
The output is as follows:
[ 0. 0. 0. 0. 0.]
Example 3
import numpy as np
x = np.zeros((5,), dtype=np.int)
print x
Now, the output would be as follows:
[0 0 0 0 0]](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-24-320.jpg)
![NumPy
24
Example 4
# custom type
import numpy as np
x = np.zeros((2,2), dtype=[('x', 'i4'), ('y', 'i4')])
print x
It should produce the following output:
[[(0, 0) (0, 0)]
[(0, 0) (0, 0)]]
numpy.ones
Returns a new array of specified size and type, filled with ones.
numpy.ones(shape, dtype=None, order='C')
The constructor takes the following parameters.
Shape Shape of an empty array in int or tuple of int
Dtype Desired output data type. Optional
Order 'C' for C-style row-major array, 'F' for FORTRAN style column-major array
Example 5
# array of five ones. Default dtype is float
import numpy as np
x = np.ones(5)
print x
The output is as follows:](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-25-320.jpg)
![NumPy
25
[ 1. 1. 1. 1. 1.]
Example 6
import numpy as np
x = np.ones([2,2], dtype=int)
print x
Now, the output would be as follows:
[[1 1]
[1 1]]](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-26-320.jpg)
![NumPy
26
In this chapter, we will discuss how to create an array from existing data.
numpy.asarray
This function is similar to numpy.array except for the fact that it has fewer parameters. This
routine is useful for converting Python sequence into ndarray.
numpy.asarray(a, dtype=None, order=None)
The constructor takes the following parameters.
a
Input data in any form such as list, list of tuples, tuples, tuple of tuples or tuple
of lists
dtype By default, the data type of input data is applied to the resultant ndarray
order C (row major) or F (column major). C is default
The following examples show how you can use the asarray function.
Example 1
# convert list to ndarray
import numpy as np
x = [1,2,3]
a = np.asarray(x)
print a
Its output would be as follows:
[1 2 3]
7. NUMPY − ARRAY FROM EXISTING DATA](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-27-320.jpg)
![NumPy
27
Example 2
# dtype is set
import numpy as np
x = [1,2,3]
a = np.asarray(x, dtype=float)
print a
Now, the output would be as follows:
[ 1. 2. 3.]
Example 3
# ndarray from tuple
import numpy as np
x = (1,2,3)
a = np.asarray(x)
print a
Its output would be:
[1 2 3]
Example 4
# ndarray from list of tuples
import numpy as np
x = [(1,2,3),(4,5)]
a = np.asarray(x)
print a
Here, the output would be as follows:
[(1, 2, 3) (4, 5)]](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-28-320.jpg)
![NumPy
28
numpy.frombuffer
This function interprets a buffer as one-dimensional array. Any object that exposes the buffer
interface is used as parameter to return an ndarray.
numpy.frombuffer(buffer, dtype=float, count=-1, offset=0)
The constructor takes the following parameters.
buffer Any object that exposes buffer interface
dtype Data type of returned ndarray. Defaults to float
count The number of items to read, default -1 means all data
offset The starting position to read from. Default is 0
Example 5
The following examples demonstrate the use of frombuffer function.
import numpy as np
s = 'Hello World'
a = np.frombuffer(s, dtype='S1')
print a
Here is its output:
['H' 'e' 'l' 'l' 'o' ' ' 'W' 'o' 'r' 'l' 'd']
numpy.fromiter
This function builds an ndarray object from any iterable object. A new one-dimensional array
is returned by this function.
numpy.fromiter(iterable, dtype, count=-1)
Here, the constructor takes the following parameters.
iterable Any iterable object
dtype
Data type of resultant array](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-29-320.jpg)
![NumPy
29
count
The number of items to be read from iterator. Default is -1 which means all data
to be read
The following examples show how to use the built-in range() function to return a list object.
An iterator of this list is used to form an ndarray object.
Example 6
# create list object using range function
import numpy as np
list = range(5)
print list
Its output is as follows:
[0, 1, 2, 3, 4]
Example 7
# obtain iterator object from list
import numpy as np
list = range(5)
it = iter(list)
# use iterator to create ndarray
x = np.fromiter(it, dtype=float)
print x
Now, the output would be as follows:
[0. 1. 2. 3. 4.]](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-30-320.jpg)
![NumPy
30
In this chapter, we will see how to create an array from numerical ranges.
numpy.arange
This function returns an ndarray object containing evenly spaced values within a given range.
The format of the function is as follows:
numpy.arange(start, stop, step, dtype)
The constructor takes the following parameters.
start The start of an interval. If omitted, defaults to 0
stop The end of an interval (not including this number)
step Spacing between values, default is 1
dtype Data type of resulting ndarray. If not given, data type of input is used
The following examples show how you can use this function.
Example 1
import numpy as np
x = np.arange(5)
print x
Its output would be as follows:
[0 1 2 3 4]
8. NUMPY − ARRAY FROM NUMERICAL RANGES](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-31-320.jpg)
![NumPy
31
Example 2
import numpy as np
# dtype set
x = np.arange(5, dtype=float)
print x
Here, the output would be:
[0. 1. 2. 3. 4.]
Example 3
# start and stop parameters set
import numpy as np
x = np.arange(10,20,2)
print x
Its output is as follows:
[10 12 14 16 18]
numpy.linspace
This function is similar to arange() function. In this function, instead of step size, the number
of evenly spaced values between the interval is specified. The usage of this function is as
follows:
numpy.linspace(start, stop, num, endpoint, retstep, dtype)
The constructor takes the following parameters.
start The starting value of the sequence
stop The end value of the sequence, included in the sequence if endpoint set to true](https://image.slidesharecdn.com/numpytutorial-190410051838/85/Numpy-tutorial-32-320.jpg)
Numpy tutorial
- 2. NumPy i AbouttheTutorial NumPy, which stands for Numerical Python, is a library consisting of multidimensional array objects and a collection of routines for processing those arrays. Using NumPy, mathematical and logical operations on arrays can be performed. This tutorial explains the basics of NumPy such as its architecture and environment. It also discusses the various array functions, types of indexing, etc. An introduction to Matplotlib is also provided. All this is explained with the help of examples for better understanding. Audience This tutorial has been prepared for those who want to learn about the basics and various functions of NumPy. It is specifically useful for algorithm developers. After completing this tutorial, you will find yourself at a moderate level of expertise from where you can take yourself to higher levels of expertise. Prerequisites You should have a basic understanding of computer programming terminologies. A basic understanding of Python and any of the programming languages is a plus. Disclaimer&Copyright Copyright 2016 by Tutorials Point (I) Pvt. Ltd. All the content and graphics published in this e-book are the property of Tutorials Point (I) Pvt. Ltd. The user of this e-book is prohibited to reuse, retain, copy, distribute or republish any contents or a part of contents of this e-book in any manner without written consent of the publisher. We strive to update the contents of our website and tutorials as timely and as precisely as possible, however, the contents may contain inaccuracies or errors. Tutorials Point (I) Pvt. Ltd. provides no guarantee regarding the accuracy, timeliness or completeness of our website or its contents including this tutorial. If you discover any errors on our website or in this tutorial, please notify us at [email protected].
- 3. NumPy ii TableofContents About the Tutorial....................................................................................................................................i Audience..................................................................................................................................................i Prerequisites............................................................................................................................................i Disclaimer & Copyright.............................................................................................................................i Table of Contents....................................................................................................................................ii 1. NUMPY − INTRODUCTION ...................................................................................................1 2. NUMPY − ENVIRONMENT....................................................................................................2 3. NUMPY − NDARRAY OBJECT................................................................................................4 4. NUMPY − DATA TYPES.........................................................................................................7 Data Type Objects (dtype).......................................................................................................................8 5. NUMPY − ARRAY ATTRIBUTES............................................................................................12 ndarray.shape.......................................................................................................................................12 ndarray.ndim ........................................................................................................................................13 numpy.itemsize.....................................................................................................................................14 numpy.flags ..........................................................................................................................................14 6. NUMPY − ARRAY CREATION ROUTINES .............................................................................16 numpy.empty........................................................................................................................................16 numpy.zeros .........................................................................................................................................17 numpy.ones ..........................................................................................................................................18 7. NUMPY − ARRAY FROM EXISTING DATA............................................................................19 numpy.asarray ......................................................................................................................................19 numpy.frombuffer ................................................................................................................................20
- 4. NumPy iii numpy.fromiter.....................................................................................................................................21 8. NUMPY − ARRAY FROM NUMERICAL RANGES...................................................................23 numpy.arange.......................................................................................................................................23 numpy.linspace.....................................................................................................................................24 numpy.logspace ....................................................................................................................................25 9. NUMPY − INDEXING & SLICING..........................................................................................27 10. NUMPY − ADVANCED INDEXING........................................................................................31 Integer Indexing....................................................................................................................................31 Boolean Array Indexing.........................................................................................................................33 11. NUMPY − BROADCASTING.................................................................................................35 12. NUMPY − ITERATING OVER ARRAY ....................................................................................38 Iteration Order......................................................................................................................................39 Modifying Array Values.........................................................................................................................42 External Loop ........................................................................................................................................42 Broadcasting Iteration...........................................................................................................................43 13. NUMPY – ARRAY MANIPULATION......................................................................................45 numpy.reshape .....................................................................................................................................47 numpy.ndarray.flat ...............................................................................................................................48 numpy.ndarray.flatten..........................................................................................................................48 numpy.ravel..........................................................................................................................................49 numpy.transpose ..................................................................................................................................50 numpy.ndarray.T...................................................................................................................................51 numpy.swapaxes ..................................................................................................................................52 numpy.rollaxis ......................................................................................................................................53 numpy.broadcast ..................................................................................................................................54
- 5. NumPy iv numpy.broadcast_to.............................................................................................................................56 numpy.expand_dims.............................................................................................................................57 numpy.squeeze.....................................................................................................................................59 numpy.concatenate ..............................................................................................................................60 numpy.stack..........................................................................................................................................61 numpy.hstack and numpy.vstack ..........................................................................................................63 numpy.split...........................................................................................................................................64 numpy.hsplit and numpy.vsplit.............................................................................................................65 numpy.resize.........................................................................................................................................66 numpy.append......................................................................................................................................68 numpy.insert.........................................................................................................................................69 numpy.delete........................................................................................................................................71 numpy.unique.......................................................................................................................................72 14. NUMPY – BINARY OPERATORS ..........................................................................................75 bitwise_and ..........................................................................................................................................75 bitwise_or.............................................................................................................................................76 numpy.invert()......................................................................................................................................77 left_shift ...............................................................................................................................................78 right_shift .............................................................................................................................................79 15. NUMPY − STRING FUNCTIONS...........................................................................................80 16. NUMPY − MATHEMATICAL FUNCTIONS ............................................................................85 Trigonometric Functions .......................................................................................................................85 Functions for Rounding .........................................................................................................................88 17. NUMPY − ARITHMETIC OPERATIONS.................................................................................91 numpy.reciprocal()................................................................................................................................93
- 6. NumPy v numpy.power() .....................................................................................................................................94 numpy.mod() ........................................................................................................................................95 18. NUMPY − STATISTICAL FUNCTIONS ...................................................................................98 numpy.amin() and numpy.amax().........................................................................................................98 numpy.ptp()..........................................................................................................................................99 numpy.percentile() .............................................................................................................................100 numpy.median()..................................................................................................................................102 numpy.mean() ....................................................................................................................................103 numpy.average().................................................................................................................................104 Standard Deviation .............................................................................................................................106 Variance..............................................................................................................................................106 19. NUMPY − SORT, SEARCH & COUNTING FUNCTIONS........................................................107 numpy.sort() .......................................................................................................................................107 numpy.argsort() ..................................................................................................................................109 numpy.lexsort()...................................................................................................................................110 numpy.argmax() and numpy.argmin().................................................................................................110 numpy.nonzero() ................................................................................................................................112 numpy.where() ...................................................................................................................................113 numpy.extract() ..................................................................................................................................114 20. NUMPY − BYTE SWAPPING..............................................................................................116 numpy.ndarray.byteswap().................................................................................................................116 21. NUMPY − COPIES & VIEWS..............................................................................................117 No Copy ..............................................................................................................................................117 View or Shallow Copy..........................................................................................................................118 Deep Copy...........................................................................................................................................120
- 7. NumPy vi 22. NUMPY − MATRIX LIBRARY..............................................................................................123 matlib.empty() ....................................................................................................................................123 numpy.matlib.zeros()..........................................................................................................................123 numpy.matlib.ones()...........................................................................................................................124 numpy.matlib.eye().............................................................................................................................124 numpy.matlib.identity()......................................................................................................................125 numpy.matlib.rand()...........................................................................................................................125 23. NUMPY − LINEAR ALGEBRA .............................................................................................127 numpy.dot()........................................................................................................................................127 numpy.vdot() ......................................................................................................................................127 numpy.inner() .....................................................................................................................................128 numpy.matmul().................................................................................................................................129 Determinant........................................................................................................................................130 numpy.linalg.solve()............................................................................................................................131 24. NUMPY − MATPLOTLIB....................................................................................................134 Sine Wave Plot ....................................................................................................................................137 subplot() .............................................................................................................................................138 bar()....................................................................................................................................................140 25. NUMPY – HISTOGRAM USING MATPLOTLIB ....................................................................141 numpy.histogram() .............................................................................................................................141 plt().....................................................................................................................................................141 26. NUMPY − I/O WITH NUMPY ............................................................................................143 numpy.save() ......................................................................................................................................143 savetxt()..............................................................................................................................................144
- 8. NumPy 7 NumPy is a Python package. It stands for 'Numerical Python'. It is a library consisting of multidimensional array objects and a collection of routines for processing of array. Numeric, the ancestor of NumPy, was developed by Jim Hugunin. Another package Numarray was also developed, having some additional functionalities. In 2005, Travis Oliphant created NumPy package by incorporating the features of Numarray into Numeric package. There are many contributors to this open source project. Operations using NumPy Using NumPy, a developer can perform the following operations: Mathematical and logical operations on arrays. Fourier transforms and routines for shape manipulation. Operations related to linear algebra. NumPy has in-built functions for linear algebra and random number generation. NumPy – A Replacement for MatLab NumPy is often used along with packages like SciPy (Scientific Python) and Mat−plotlib (plotting library). This combination is widely used as a replacement for MatLab, a popular platform for technical computing. However, Python alternative to MatLab is now seen as a more modern and complete programming language. It is open source, which is an added advantage of NumPy. 1. NUMPY − INTRODUCTION
- 9. NumPy 8 Standard Python distribution doesn't come bundled with NumPy module. A lightweight alternative is to install NumPy using popular Python package installer, pip. pip install numpy The best way to enable NumPy is to use an installable binary package specific to your operating system. These binaries contain full SciPy stack (inclusive of NumPy, SciPy, matplotlib, IPython, SymPy and nose packages along with core Python). Windows Anaconda (from https://www.continuum.io) is a free Python distribution for SciPy stack. It is also available for Linux and Mac. Canopy (https://www.enthought.com/products/canopy/) is available as free as well as commercial distribution with full SciPy stack for Windows, Linux and Mac. Python (x,y): It is a free Python distribution with SciPy stack and Spyder IDE for Windows OS. (Downloadable from http://python-xy.github.io/) Linux Package managers of respective Linux distributions are used to install one or more packages in SciPy stack. For Ubuntu sudo apt-get install python-numpy python-scipy python-matplotlibipythonipython- notebook python-pandas python-sympy python-nose For Fedora sudo yum install numpyscipy python-matplotlibipython python-pandas sympy python- nose atlas-devel Building from Source Core Python (2.6.x, 2.7.x and 3.2.x onwards) must be installed with distutils and zlib module should be enabled. GNU gcc (4.2 and above) C compiler must be available. 2. NUMPY − ENVIRONMENT
- 10. NumPy 9 To install NumPy, run the following command. Python setup.py install To test whether NumPy module is properly installed, try to import it from Python prompt. import numpy If it is not installed, the following error message will be displayed. Traceback (most recent call last): File "<pyshell#0>", line 1, in <module> import numpy ImportError: No module named 'numpy' Alternatively, NumPy package is imported using the following syntax: import numpy as np
- 11. NumPy 10 The most important object defined in NumPy is an N-dimensional array type called ndarray. It describes the collection of items of the same type. Items in the collection can be accessed using a zero-based index. Every item in an ndarray takes the same size of block in the memory. Each element in ndarray is an object of data-type object (called dtype). Any item extracted from ndarray object (by slicing) is represented by a Python object of one of array scalar types. The following diagram shows a relationship between ndarray, data type object (dtype) and array scalar type: An instance of ndarray class can be constructed by different array creation routines described later in the tutorial. The basic ndarray is created using an array function in NumPy as follows: numpy.array It creates an ndarray from any object exposing array interface, or from any method that returns an array. numpy.array(object, dtype=None, copy=True, order=None, subok=False, ndmin=0) 3. NUMPY − NDARRAY OBJECT
- 12. NumPy 11 The above constructor takes the following parameters: object Any object exposing the array interface method returns an array, or any (nested) sequence dtype Desired data type of array, optional copy Optional. By default (true), the object is copied order C (row major) or F (column major) or A (any) (default) subok By default, returned array forced to be a base class array. If true, sub-classes passed through ndimin Specifies minimum dimensions of resultant array Take a look at the following examples to understand better. Example 1 import numpy as np a=np.array([1,2,3]) print a The output is as follows: [1, 2, 3] Example 2 # more than one dimensions import numpy as np
- 13. NumPy 12 a = np.array([[1, 2], [3, 4]]) print a The output is as follows: [[1, 2] [3, 4]] Example 3 # minimum dimensions import numpy as np a=np.array([1, 2, 3,4,5], ndmin=2) print a The output is as follows: [[1, 2, 3, 4, 5]] Example 4 # dtype parameter import numpy as np a = np.array([1, 2, 3], dtype=complex) print a The output is as follows: [ 1.+0.j, 2.+0.j, 3.+0.j] The ndarray object consists of contiguous one-dimensional segment of computer memory, combined with an indexing scheme that maps each item to a location in the memory block. The memory block holds the elements in a row-major order (C style) or a column-major order (FORTRAN or MatLab style).
- 14. NumPy 13 NumPy supports a much greater variety of numerical types than Python does. The following table shows different scalar data types defined in NumPy. Data Types Description bool_ Boolean (True or False) stored as a byte int_ Default integer type (same as C long; normally either int64 or int32) intc Identical to C int (normally int32 or int64) intp Integer used for indexing (same as C ssize_t; normally either int32 or int64) int8 Byte (-128 to 127) int16 Integer (-32768 to 32767) int32 Integer (-2147483648 to 2147483647) int64 Integer (-9223372036854775808 to 9223372036854775807) uint8 Unsigned integer (0 to 255) uint16 Unsigned integer (0 to 65535) uint32 Unsigned integer (0 to 4294967295) uint64 Unsigned integer (0 to 18446744073709551615) float_ Shorthand for float64 float16 Half precision float: sign bit, 5 bits exponent, 10 bits mantissa float32 Single precision float: sign bit, 8 bits exponent, 23 bits mantissa float64 Double precision float: sign bit, 11 bits exponent, 52 bits mantissa complex_ Shorthand for complex128 complex64 Complex number, represented by two 32-bit floats (real and imaginary components) complex128 Complex number, represented by two 64-bit floats (real and imaginary components) 4. NUMPY − DATA TYPES
- 15. NumPy 14 NumPy numerical types are instances of dtype (data-type) objects, each having unique characteristics. The dtypes are available as np.bool_, np.float32, etc. DataTypeObjects(dtype) A data type object describes interpretation of fixed block of memory corresponding to an array, depending on the following aspects: Type of data (integer, float or Python object) Size of data Byte order (little-endian or big-endian) In case of structured type, the names of fields, data type of each field and part of the memory block taken by each field If data type is a subarray, its shape and data type The byte order is decided by prefixing '<' or '>' to data type. '<' means that encoding is little- endian (least significant is stored in smallest address). '>' means that encoding is big-endian (most significant byte is stored in smallest address). A dtype object is constructed using the following syntax: numpy.dtype(object, align, copy) The parameters are: Object: To be converted to data type object Align: If true, adds padding to the field to make it similar to C-struct Copy: Makes a new copy of dtype object. If false, the result is reference to built-in data type object Example 1 # using array-scalar type import numpy as np dt=np.dtype(np.int32) print dt The output is as follows: int32
- 16. NumPy 15 Example 2 #int8, int16, int32, int64 can be replaced by equivalent string 'i1', 'i2','i4', etc. import numpy as np dt = np.dtype('i4') print dt The output is as follows: int32 Example 3 # using endian notation import numpy as np dt = np.dtype('>i4') print dt The output is as follows: >i4 The following examples show the use of structured data type. Here, the field name and the corresponding scalar data type is to be declared. Example 4 # first create structured data type import numpy as np dt = np.dtype([('age',np.int8)]) print dt The output is as follows: [('age', 'i1')] Example 5 # now apply it to ndarray object
- 17. NumPy 16 import numpy as np dt = np.dtype([('age',np.int8)]) a = np.array([(10,),(20,),(30,)], dtype=dt) print a The output is as follows: [(10,) (20,) (30,)] Example 6 # file name can be used to access content of age column import numpy as np dt = np.dtype([('age',np.int8)]) a = np.array([(10,),(20,),(30,)], dtype=dt) print a['age'] The output is as follows: [10 20 30] Example 7 The following examples define a structured data type called student with a string field 'name', an integer field 'age' and a float field 'marks'. This dtype is applied to ndarray object. import numpy as np student=np.dtype([('name','S20'), ('age', 'i1'), ('marks', 'f4')]) print student The output is as follows: [('name', 'S20'), ('age', 'i1'), ('marks', '<f4')]) Example 8 import numpy as np student=np.dtype([('name','S20'), ('age', 'i1'), ('marks', 'f4')]) a = np.array([('abc', 21, 50),('xyz', 18, 75)], dtype=student)
- 18. NumPy 17 print a The output is as follows: [('abc', 21, 50.0), ('xyz', 18, 75.0)] Each built-in data type has a character code that uniquely identifies it. 'b': boolean 'i': (signed) integer 'u': unsigned integer 'f': floating-point 'c': complex-floating point 'm': timedelta 'M': datetime 'O': (Python) objects 'S', 'a': (byte-)string 'U': Unicode 'V': raw data (void)
- 19. NumPy 18 In this chapter, we will discuss the various array attributes of NumPy. ndarray.shape This array attribute returns a tuple consisting of array dimensions. It can also be used to resize the array. Example 1 import numpy as np a=np.array([[1,2,3],[4,5,6]]) print a.shape The output is as follows: (2, 3) Example 2 # this resizes the ndarray import numpy as np a=np.array([[1,2,3],[4,5,6]]) a.shape=(3,2) print a The output is as follows: [[1 2] [3 4] [5 6]] Example 3 NumPy also provides a reshape function to resize an array. import numpy as np 5. NUMPY − ARRAY ATTRIBUTES
- 20. NumPy 19 a = np.array([[1,2,3],[4,5,6]]) b = a.reshape(3,2) print b The output is as follows: [[1 2] [3 4] [5 6]] ndarray.ndim This array attribute returns the number of array dimensions. Example 4 # an array of evenly spaced numbers import numpy as np a = np.arange(24) print a The output is as follows: [0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23] Example 5 # this is one dimensional array import numpy as np a = np.arange(24) a.ndim # now reshape it b = a.reshape(2,4,3) print b # b is having three dimensions The output is as follows:
- 21. NumPy 20 [[[ 0, 1, 2] [ 3, 4, 5] [ 6, 7, 8] [ 9, 10, 11]] [[12, 13, 14] [15, 16, 17] [18, 19, 20] [21, 22, 23]]] numpy.itemsize This array attribute returns the length of each element of array in bytes. Example 6 # dtype of array is int8 (1 byte) import numpy as np x = np.array([1,2,3,4,5], dtype=np.int8) print x.itemsize The output is as follows: 1 Example 7 # dtype of array is now float32 (4 bytes) import numpy as np x = np.array([1,2,3,4,5], dtype=np.float32) print x.itemsize The output is as follows: 4
- 22. NumPy 21 numpy.flags The ndarray object has the following attributes. Its current values are returned by this function. C_CONTIGUOUS (C) The data is in a single, C-style contiguous segment F_CONTIGUOUS (F) The data is in a single, Fortran-style contiguous segment OWNDATA (O) The array owns the memory it uses or borrows it from another object WRITEABLE (W) The data area can be written to. Setting this to False locks the data, making it read-only ALIGNED (A) The data and all elements are aligned appropriately for the hardware UPDATEIFCOPY (U) This array is a copy of some other array. When this array is deallocated, the base array will be updated with the contents of this array Example 8 The following example shows the current values of flags. import numpy as np x = np.array([1,2,3,4,5]) print x.flags The output is as follows: C_CONTIGUOUS : True F_CONTIGUOUS : True OWNDATA : True WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False
- 23. NumPy 22 A new ndarray object can be constructed by any of the following array creation routines or using a low-level ndarray constructor. numpy.empty It creates an uninitialized array of specified shape and dtype. It uses the following constructor: numpy.empty(shape, dtype=float, order='C') The constructor takes the following parameters. Shape Shape of an empty array in int or tuple of int Dtype Desired output data type. Optional Order 'C' for C-style row-major array, 'F' for FORTRAN style column-major array Example 1 The following code shows an example of an empty array. import numpy as np x = np.empty([3,2], dtype=int) print x The output is as follows: [[22649312 1701344351] [1818321759 1885959276] [16779776 156368896]] Note: The elements in an array show random values as they are not initialized. 6. NUMPY − ARRAY CREATION ROUTINES
- 24. NumPy 23 numpy.zeros Returns a new array of specified size, filled with zeros. numpy.zeros(shape, dtype=float, order='C') The constructor takes the following parameters. Shape Shape of an empty array in int or sequence of int Dtype Desired output data type. Optional Order 'C' for C-style row-major array, 'F' for FORTRAN style column-major array Example 2 # array of five zeros. Default dtype is float import numpy as np x = np.zeros(5) print x The output is as follows: [ 0. 0. 0. 0. 0.] Example 3 import numpy as np x = np.zeros((5,), dtype=np.int) print x Now, the output would be as follows: [0 0 0 0 0]
- 25. NumPy 24 Example 4 # custom type import numpy as np x = np.zeros((2,2), dtype=[('x', 'i4'), ('y', 'i4')]) print x It should produce the following output: [[(0, 0) (0, 0)] [(0, 0) (0, 0)]] numpy.ones Returns a new array of specified size and type, filled with ones. numpy.ones(shape, dtype=None, order='C') The constructor takes the following parameters. Shape Shape of an empty array in int or tuple of int Dtype Desired output data type. Optional Order 'C' for C-style row-major array, 'F' for FORTRAN style column-major array Example 5 # array of five ones. Default dtype is float import numpy as np x = np.ones(5) print x The output is as follows:
- 26. NumPy 25 [ 1. 1. 1. 1. 1.] Example 6 import numpy as np x = np.ones([2,2], dtype=int) print x Now, the output would be as follows: [[1 1] [1 1]]
- 27. NumPy 26 In this chapter, we will discuss how to create an array from existing data. numpy.asarray This function is similar to numpy.array except for the fact that it has fewer parameters. This routine is useful for converting Python sequence into ndarray. numpy.asarray(a, dtype=None, order=None) The constructor takes the following parameters. a Input data in any form such as list, list of tuples, tuples, tuple of tuples or tuple of lists dtype By default, the data type of input data is applied to the resultant ndarray order C (row major) or F (column major). C is default The following examples show how you can use the asarray function. Example 1 # convert list to ndarray import numpy as np x = [1,2,3] a = np.asarray(x) print a Its output would be as follows: [1 2 3] 7. NUMPY − ARRAY FROM EXISTING DATA
- 28. NumPy 27 Example 2 # dtype is set import numpy as np x = [1,2,3] a = np.asarray(x, dtype=float) print a Now, the output would be as follows: [ 1. 2. 3.] Example 3 # ndarray from tuple import numpy as np x = (1,2,3) a = np.asarray(x) print a Its output would be: [1 2 3] Example 4 # ndarray from list of tuples import numpy as np x = [(1,2,3),(4,5)] a = np.asarray(x) print a Here, the output would be as follows: [(1, 2, 3) (4, 5)]
- 29. NumPy 28 numpy.frombuffer This function interprets a buffer as one-dimensional array. Any object that exposes the buffer interface is used as parameter to return an ndarray. numpy.frombuffer(buffer, dtype=float, count=-1, offset=0) The constructor takes the following parameters. buffer Any object that exposes buffer interface dtype Data type of returned ndarray. Defaults to float count The number of items to read, default -1 means all data offset The starting position to read from. Default is 0 Example 5 The following examples demonstrate the use of frombuffer function. import numpy as np s = 'Hello World' a = np.frombuffer(s, dtype='S1') print a Here is its output: ['H' 'e' 'l' 'l' 'o' ' ' 'W' 'o' 'r' 'l' 'd'] numpy.fromiter This function builds an ndarray object from any iterable object. A new one-dimensional array is returned by this function. numpy.fromiter(iterable, dtype, count=-1) Here, the constructor takes the following parameters. iterable Any iterable object dtype Data type of resultant array
- 30. NumPy 29 count The number of items to be read from iterator. Default is -1 which means all data to be read The following examples show how to use the built-in range() function to return a list object. An iterator of this list is used to form an ndarray object. Example 6 # create list object using range function import numpy as np list = range(5) print list Its output is as follows: [0, 1, 2, 3, 4] Example 7 # obtain iterator object from list import numpy as np list = range(5) it = iter(list) # use iterator to create ndarray x = np.fromiter(it, dtype=float) print x Now, the output would be as follows: [0. 1. 2. 3. 4.]
- 31. NumPy 30 In this chapter, we will see how to create an array from numerical ranges. numpy.arange This function returns an ndarray object containing evenly spaced values within a given range. The format of the function is as follows: numpy.arange(start, stop, step, dtype) The constructor takes the following parameters. start The start of an interval. If omitted, defaults to 0 stop The end of an interval (not including this number) step Spacing between values, default is 1 dtype Data type of resulting ndarray. If not given, data type of input is used The following examples show how you can use this function. Example 1 import numpy as np x = np.arange(5) print x Its output would be as follows: [0 1 2 3 4] 8. NUMPY − ARRAY FROM NUMERICAL RANGES
- 32. NumPy 31 Example 2 import numpy as np # dtype set x = np.arange(5, dtype=float) print x Here, the output would be: [0. 1. 2. 3. 4.] Example 3 # start and stop parameters set import numpy as np x = np.arange(10,20,2) print x Its output is as follows: [10 12 14 16 18] numpy.linspace This function is similar to arange() function. In this function, instead of step size, the number of evenly spaced values between the interval is specified. The usage of this function is as follows: numpy.linspace(start, stop, num, endpoint, retstep, dtype) The constructor takes the following parameters. start The starting value of the sequence stop The end value of the sequence, included in the sequence if endpoint set to true
- 33. NumPy 32 num The number of evenly spaced samples to be generated. Default is 50 endpoint True by default, hence the stop value is included in the sequence. If false, it is not included retstep If true, returns samples and step between the consecutive numbers dtype Data type of output ndarray
- 34. NumPy 33 End of ebook preview If you liked what you saw… Buy it from our store @ https://store.tutorialspoint.com