Chapter 2. NumPy Arrays and Vectorized Computation

NumPy is the fundamental package supported for presenting and computing data with high performance in Python. It provides some interesting features as follows:

• Extension package to Python for multidimensional arrays (ndarrays), various derived objects (such as masked arrays), matrices providing vectorization operations, and broadcasting capabilities. Vectorization can significantly increase the performance of array computations by taking advantage of Single Instruction Multiple Data (SIMD) instruction sets in modern CPUs.
• Fast and convenient operations on arrays of data, including mathematical manipulation, basic statistical operations, sorting, selecting, linear algebra, random number generation, discrete Fourier transforms, and so on.
• Efficiency tools that are closer to hardware because of integrating C/C++/Fortran code.

NumPy is a good starting package for you to get familiar with arrays and array-oriented computing in data analysis. Also, it is the basic step to learn other, more effective tools such as Pandas, which we will see in the next chapter. We will be using NumPy version 1.9.1.

NumPy arrays

An array can be used to contain values of a data object in an experiment or simulation step, pixels of an image, or a signal recorded by a measurement device. For example, the latitude of the Eiffel Tower, Paris is 48.858598 and the longitude is 2.294495. It can be presented in a NumPy array object as p:

>>> import numpy as np
>>> p = np.array([48.858598, 2.294495])
>>> p
array([48.858598, 2.294495])

This is a manual construction of an array using the np.array function. The standard convention to import NumPy is as follows:

>>> import numpy as np

You can, of course, put from numpy import * in your code to avoid having to write np. However, you should be careful with this habit because of the potential code conflicts (further information on code conventions can be found in the Python Style Guide, also known as PEP8, at https://www.python.org/dev/peps/pep-0008/).

There are two requirements of a NumPy array: a fixed size at creation and a uniform, fixed data type, with a fixed size in memory. The following functions help you to get information on the p matrix:

>>> p.ndim    # getting dimension of array p
1
>>> p.shape   # getting size of each array dimension
(2,)
>>> len(p)    # getting dimension length of array p
2
>>> p.dtype    # getting data type of array p
dtype('float64')

Data types

There are five basic numerical types including Booleans (bool), integers (int), unsigned integers (uint), floating point (float), and complex. They indicate how many bits are needed to represent elements of an array in memory. Besides that, NumPy also has some types, such as intc and intp, that have different bit sizes depending on the platform.

See the following table for a listing of NumPy's supported data types:

Type	Type code	Description	Range of value
bool		Boolean stored as a byte	True/False
intc		Similar to C int (int32 or int 64)
intp		Integer used for indexing (same as C size_t)
int8, uint8	i1, u1	Signed and unsigned 8-bit integer types	int8: (-128 to 127) uint8: (0 to 255)
int16, uint16	i2, u2	Signed and unsigned 16-bit integer types	int16: (-32768 to 32767) uint16: (0 to 65535)
int32, uint32	I4, u4	Signed and unsigned 32-bit integer types	int32: (-2147483648 to 2147483647 uint32: (0 to 4294967295)
int64, uinit64	i8, u8	Signed and unsigned 64-bit integer types	Int64: (-9223372036854775808 to 9223372036854775807) uint64: (0 to 18446744073709551615)
float16	f2	Half precision float: sign bit, 5 bits exponent, and 10b bits mantissa
float32	f4 / f	Single precision float: sign bit, 8 bits exponent, and 23 bits mantissa
float64	f8 / d	Double precision float: sign bit, 11 bits exponent, and 52 bits mantissa
complex64, complex128, complex256	c8, c16, c32	Complex numbers represented by two 32-bit, 64-bit, and 128-bit floats
object	0	Python object type
string_	S	Fixed-length string type	Declare a string dtype with length 10, using S10
unicode_	U	Fixed-length Unicode type	Similar to string_ example, we have 'U10'

We can easily convert or cast an array from one dtype to another using the astype method:

>>> a = np.array([1, 2, 3, 4])
>>> a.dtype
dtype('int64')
>>> float_b = a.astype(np.float64)
>>> float_b.dtype
dtype('float64')

Note

The astype function will create a new array with a copy of data from an old array, even though the new dtype is similar to the old one.

Array creation

There are various functions provided to create an array object. They are very useful for us to create and store data in a multidimensional array in different situations.

Now, in the following table we will summarize some of NumPy's common functions and their use by examples for array creation:

Function	Description	Example
empty, empty_like	Create a new array of the given shape and type, without initializing elements	>>> np.empty([3,2], dtype=np.float64) array([[0., 0.], [0., 0.], [0., 0.]]) >>> a = np.array([[1, 2], [4, 3]]) >>> np.empty_like(a) array([[0, 0], [0, 0]])
eye, identity	Create a NxN identity matrix with ones on the diagonal and zero elsewhere	>>> np.eye(2, dtype=np.int) array([[1, 0], [0, 1]])
ones, ones_like	Create a new array with the given shape and type, filled with 1s for all elements	>>> np.ones(5) array([1., 1., 1., 1., 1.]) >>> np.ones(4, dtype=np.int) array([1, 1, 1, 1]) >>> x = np.array([[0,1,2], [3,4,5]]) >>> np.ones_like(x) array([[1, 1, 1],[1, 1, 1]])
zeros, zeros_like	This is similar to ones, ones_like, but initializing elements with 0s instead	>>> np.zeros(5) array([0., 0., 0., 0-, 0.]) >>> np.zeros(4, dtype=np.int) array([0, 0, 0, 0]) >>> x = np.array([[0, 1, 2], [3, 4, 5]]) >>> np.zeros_like(x) array([[0, 0, 0],[0, 0, 0]])
arange	Create an array with even spaced values in a given interval	>>> np.arange(2, 5) array([2, 3, 4]) >>> np.arange(4, 12, 5) array([4, 9])
full, full_like	Create a new array with the given shape and type, filled with a selected value	>>> np.full((2,2), 3, dtype=np.int) array([[3, 3], [3, 3]]) >>> x = np.ones(3) >>> np.full_like(x, 2) array([2., 2., 2.])
array	Create an array from the existing data	>>> np.array([[1.1, 2.2, 3.3], [4.4, 5.5, 6.6]]) array([1.1, 2.2, 3.3], [4.4, 5.5, 6.6]])
asarray	Convert the input to an array	>>> a = [3.14, 2.46] >>> np.asarray(a) array([3.14, 2.46])
copy	Return an array copy of the given object	>>> a = np.array([[1, 2], [3, 4]]) >>> np.copy(a) array([[1, 2], [3, 4]])
fromstring	Create 1-D array from a string or text	>>> np.fromstring('3.14 2.17', dtype=np.float, sep=' ') array([3.14, 2.17])

Indexing and slicing

As with other Python sequence types, such as lists, it is very easy to access and assign a value of each array's element:

>>> a = np.arange(7)
>>> a
array([0, 1, 2, 3, 4, 5, 6])
>>> a[1], a [4], a[-1]
(1, 4, 6)

Note

In Python, array indices start at 0. This is in contrast to Fortran or Matlab, where indices begin at 1.

As another example, if our array is multidimensional, we need tuples of integers to index an item:

>>> a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
>>> a[0, 2]      # first row, third column
3
>>> a[0, 2] = 10
>>> a
array([[1, 2, 10], [4, 5, 6], [7, 8, 9]])
>>> b = a[2]
>>> b
array([7, 8, 9])
>>> c = a[:2]
>>> c
array([[1, 2, 10], [4, 5, 6]])

We call b and c as array slices, which are views on the original one. It means that the data is not copied to b or c, and whenever we modify their values, it will be reflected in the array a as well:

>>> b[-1] = 11
>>> a
array([[1, 2, 10], [4, 5, 6], [7, 8, 11]])

Note

We use a colon (:) character to take the entire axis when we omit the index number.

Fancy indexing

Besides indexing with slices, NumPy also supports indexing with Boolean or integer arrays (masks). This method is called fancy indexing. It creates copies, not views.

First, we take a look at an example of indexing with a Boolean mask array:

>>> a = np.array([3, 5, 1, 10])
>>> b = (a % 5 == 0)
>>> b
array([False, True, False, True], dtype=bool)
>>> c = np.array([[0, 1], [2, 3], [4, 5], [6, 7]])
>>> c[b]
array([[2, 3], [6, 7]])

The second example is an illustration of using integer masks on arrays:

>>> a = np.array([[1, 2, 3, 4], 
 [5, 6, 7, 8], 
 [9, 10, 11, 12],
 [13, 14, 15, 16]])
>>> a[[2, 1]]
array([[9, 10, 11, 12], [5, 6, 7, 8]])
>>> a[[-2, -1]]          # select rows from the end
array([[ 9, 10, 11, 12], [13, 14, 15, 16]])
>>> a[[2, 3], [0, 1]]    # take elements at (2, 0) and (3, 1)
array([9, 14])

Note

The mask array must have the same length as the axis that it's indexing.

Tip

Downloading the example code

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Numerical operations on arrays

We are getting familiar with creating and accessing ndarrays. Now, we continue to the next step, applying some mathematical operations to array data without writing any for loops, of course, with higher performance.

Scalar operations will propagate the value to each element of the array:

>>> a = np.ones(4)
>>> a * 2
array([2., 2., 2., 2.])
>>> a + 3
array([4., 4., 4., 4.])

All arithmetic operations between arrays apply the operation element wise:

>>> a = np.ones([2, 4])
>>> a * a
array([[1., 1., 1., 1.], [1., 1., 1., 1.]])
>>> a + a
array([[2., 2., 2., 2.], [2., 2., 2., 2.]])

Also, here are some examples of comparisons and logical operations:

>>> a = np.array([1, 2, 3, 4])
>>> b = np.array([1, 1, 5, 3])
>>> a == b
array([True, False, False, False], dtype=bool)

>>> np.array_equal(a, b)      # array-wise comparison
False

>>> c = np.array([1, 0])
>>> d = np.array([1, 1])
>>> np.logical_and(c, d)      # logical operations
array([True, False])

Array functions

Many helpful array functions are supported in NumPy for analyzing data. We will list some part of them that are common in use. Firstly, the transposing function is another kind of reshaping form that returns a view on the original data array without copying anything:

>>> a = np.array([[0, 5, 10], [20, 25, 30]])
>>> a.reshape(3, 2)
array([[0, 5], [10, 20], [25, 30]])
>>> a.T
array([[0, 20], [5, 25], [10, 30]])

In general, we have the swapaxes method that takes a pair of axis numbers and returns a view on the data, without making a copy:

>>> a = np.array([[[0, 1, 2], [3, 4, 5]], 
 [[6, 7, 8], [9, 10, 11]]])
>>> a.swapaxes(1, 2)
array([[[0, 3],
    [1, 4],
    [2, 5]],
   [[6, 9],
    [7, 10],
    [8, 11]]])

The transposing function is used to do matrix computations; for example, computing the inner matrix product XT.X using np.dot:

>>> a = np.array([[1, 2, 3],[4,5,6]])
>>> np.dot(a.T, a)
array([[17, 22, 27],
   [22, 29, 36],
   [27, 36, 45]])

Sorting data in an array is also an important demand in processing data. Let's take a look at some sorting functions and their use:

>>> a = np.array ([[6, 34, 1, 6], [0, 5, 2, -1]])

>>> np.sort(a)     # sort along the last axis
array([[1, 6, 6, 34], [-1, 0, 2, 5]])

>>> np.sort(a, axis=0)    # sort along the first axis
array([[0, 5, 1, -1], [6, 34, 2, 6]])

>>> b = np.argsort(a)    # fancy indexing of sorted array
>>> b
array([[2, 0, 3, 1], [3, 0, 2, 1]])
>>> a[0][b[0]]
array([1, 6, 6, 34])

>>> np.argmax(a)    # get index of maximum element
1

See the following table for a listing of array functions:

Function	Description	Example
sin, cos, tan, cosh, sinh, tanh, arcos, arctan, deg2rad	Trigonometric and hyperbolic functions	>>> a = np.array([0.,30., 45.]) >>> np.sin(a * np.pi / 180) array([0., 0.5, 0.7071678])
around, round, rint, fix, floor, ceil, trunc	Rounding elements of an array to the given or nearest number	>>> a = np.array([0.34, 1.65]) >>> np.round(a) array([0., 2.])
sqrt, square, exp, expm1, exp2, log, log10, log1p, logaddexp	Computing the exponents and logarithms of an array	>>> np.exp(np.array([2.25, 3.16])) array([9.4877, 23.5705])
add, negative, multiply, devide, power, substract, mod, modf, remainder	Set of arithmetic functions on arrays	>>> a = np.arange(6) >>> x1 = a.reshape(2,3) >>> x2 = np.arange(3) >>> np.multiply(x1, x2) array([[0,1,4],[0,4,10]])
greater, greater_equal, less, less_equal, equal, not_equal	Perform elementwise comparison: >, >=, <, <=, ==, !=	>>> np.greater(x1, x2) array([[False, False, False], [True, True, True]], dtype = bool)

Data processing using arrays

With the NumPy package, we can easily solve many kinds of data processing tasks without writing complex loops. It is very helpful for us to control our code as well as the performance of the program. In this part, we want to introduce some mathematical and statistical functions.

See the following table for a listing of mathematical and statistical functions:

Function	Description	Example
sum	Calculate the sum of all the elements in an array or along the axis	>>> a = np.array([[2,4], [3,5]]) >>> np.sum(a, axis=0) array([5, 9])
prod	Compute the product of array elements over the given axis	>>> np.prod(a, axis=1) array([8, 15])
diff	Calculate the discrete difference along the given axis	>>> np.diff(a, axis=0) array([[1,1]])
gradient	Return the gradient of an array	>>> np.gradient(a) [array([[1., 1.], [1., 1.]]), array([[2., 2.], [2., 2.]])]
cross	Return the cross product of two arrays	>>> b = np.array([[1,2], [3,4]]) >>> np.cross(a,b) array([0, -3])
std, var	Return standard deviation and variance of arrays	>>> np.std(a) 1.1180339 >>> np.var(a) 1.25
mean	Calculate arithmetic mean of an array	>>> np.mean(a) 3.5
where	Return elements, either from x or y, that satisfy a condition	>>> np.where([[True, True], [False, True]], [[1,2],[3,4]], [[5,6],[7,8]]) array([[1,2], [7, 4]])
unique	Return the sorted unique values in an array	>>> id = np.array(['a', 'b', 'c', 'c', 'd']) >>> np.unique(id) array(['a', 'b', 'c', 'd'], dtype='|S1')
intersect1d	Compute the sorted and common elements in two arrays	>>> a = np.array(['a', 'b', 'a', 'c', 'd', 'c']) >>> b = np.array(['a', 'xyz', 'klm', 'd']) >>> np.intersect1d(a,b) array(['a', 'd'], dtype='|S3')

Loading and saving data

We can also save and load data to and from a disk, either in text or binary format, by using different supported functions in NumPy package.

Saving an array

Arrays are saved by default in an uncompressed raw binary format, with the file extension .npy by the np.save function:

>>> a = np.array([[0, 1, 2], [3, 4, 5]])
>>> np.save('test1.npy', a)

Note

The library automatically assigns the .npy extension, if we omit it.

If we want to store several arrays into a single file in an uncompressed .npz format, we can use the np.savez function, as shown in the following example:

>>> a = np.arange(4)
>>> b = np.arange(7)
>>> np.savez('test2.npz', arr0=a, arr1=b)

The .npz file is a zipped archive of files named after the variables they contain. When we load an .npz file, we get back a dictionary-like object that can be queried for its lists of arrays:

>>> dic = np.load('test2.npz')
>>> dic['arr0']
array([0, 1, 2, 3])

Another way to save array data into a file is using the np.savetxt function that allows us to set format properties in the output file:

>>> x = np.arange(4)
>>> # e.g., set comma as separator between elements
>>> np.savetxt('test3.out', x, delimiter=',')

Loading an array

We have two common functions such as np.load and np.loadtxt, which correspond to the saving functions, for loading an array:

>>> np.load('test1.npy')
array([[0, 1, 2], [3, 4, 5]])
>>> np.loadtxt('test3.out', delimiter=',')
array([0., 1., 2., 3.])

Similar to the np.savetxt function, the np.loadtxt function also has a lot of options for loading an array from a text file.

Loading and saving data

We can also save and load data to and from a disk, either in text or binary format, by using different supported functions in NumPy package.

Saving an array

Arrays are saved by default in an uncompressed raw binary format, with the file extension .npy by the np.save function:

>>> a = np.array([[0, 1, 2], [3, 4, 5]])
>>> np.save('test1.npy', a)

Note

The library automatically assigns the .npy extension, if we omit it.

If we want to store several arrays into a single file in an uncompressed .npz format, we can use the np.savez function, as shown in the following example:

>>> a = np.arange(4)
>>> b = np.arange(7)
>>> np.savez('test2.npz', arr0=a, arr1=b)

The .npz file is a zipped archive of files named after the variables they contain. When we load an .npz file, we get back a dictionary-like object that can be queried for its lists of arrays:

>>> dic = np.load('test2.npz')
>>> dic['arr0']
array([0, 1, 2, 3])

Another way to save array data into a file is using the np.savetxt function that allows us to set format properties in the output file:

>>> x = np.arange(4)
>>> # e.g., set comma as separator between elements
>>> np.savetxt('test3.out', x, delimiter=',')

Loading an array

We have two common functions such as np.load and np.loadtxt, which correspond to the saving functions, for loading an array:

>>> np.load('test1.npy')
array([[0, 1, 2], [3, 4, 5]])
>>> np.loadtxt('test3.out', delimiter=',')
array([0., 1., 2., 3.])

Similar to the np.savetxt function, the np.loadtxt function also has a lot of options for loading an array from a text file.

Saving an array

Arrays are

saved by default in an uncompressed raw binary format, with the file extension .npy by the np.save function:

>>> a = np.array([[0, 1, 2], [3, 4, 5]])
>>> np.save('test1.npy', a)

Note

The library automatically assigns the .npy extension, if we omit it.

If we want to store several arrays into a single file in an uncompressed .npz format, we can use the np.savez function, as shown in the following example:

>>> a = np.arange(4)
>>> b = np.arange(7)
>>> np.savez('test2.npz', arr0=a, arr1=b)

The .npz file is a zipped archive of files named after the variables they contain. When we load an .npz file, we get back a dictionary-like object that can be queried for its lists of arrays:

>>> dic = np.load('test2.npz')
>>> dic['arr0']
array([0, 1, 2, 3])

Another way to save array data into a file is using the np.savetxt function that allows us to set format properties in the output file:

>>> x = np.arange(4)
>>> # e.g., set comma as separator between elements
>>> np.savetxt('test3.out', x, delimiter=',')

Loading an array

We have two common functions such as np.load and np.loadtxt, which correspond to the saving functions, for loading an array:

>>> np.load('test1.npy')
array([[0, 1, 2], [3, 4, 5]])
>>> np.loadtxt('test3.out', delimiter=',')
array([0., 1., 2., 3.])

Similar to the np.savetxt function, the np.loadtxt function also has a lot of options for loading an array from a text file.

Loading an array

We have two

common functions such as np.load and np.loadtxt, which correspond to the saving functions, for loading an array:

>>> np.load('test1.npy')
array([[0, 1, 2], [3, 4, 5]])
>>> np.loadtxt('test3.out', delimiter=',')
array([0., 1., 2., 3.])

Similar to the np.savetxt function, the np.loadtxt function also has a lot of options for loading an array from a text file.

Linear algebra with NumPy

Linear algebra is a branch of mathematics concerned with vector spaces and the mappings between those spaces. NumPy has a package called linalg that supports powerful linear algebra functions. We can use these functions to find eigenvalues and eigenvectors or to perform singular value decomposition:

>>> A = np.array([[1, 4, 6],
    [5, 2, 2],
    [-1, 6, 8]])
>>> w, v = np.linalg.eig(A)
>>> w                           # eigenvalues
array([-0.111 + 1.5756j, -0.111 – 1.5756j, 11.222+0.j])
>>> v                           # eigenvector
array([[-0.0981 + 0.2726j, -0.0981 – 0.2726j, 0.5764+0.j],
    [0.7683+0.j, 0.7683-0.j, 0.4591+0.j],
    [-0.5656 – 0.0762j, -0.5656 + 0.00763j, 0.6759+0.j]])

The function is implemented using the geev Lapack routines that compute the eigenvalues and eigenvectors of general square matrices.

Another common problem is solving linear systems such as Ax = b with A as a matrix and x and b as vectors. The problem can be solved easily using the numpy.linalg.solve function:

>>> A = np.array([[1, 4, 6], [5, 2, 2], [-1, 6, 8]])
>>> b = np.array([[1], [2], [3]])
>>> x = np.linalg.solve(A, b)
>>> x
array([[-1.77635e-16], [2.5], [-1.5]])

The following table will summarise some commonly used functions in the numpy.linalg package:

Function	Description	Example
dot	Calculate the dot product of two arrays	>>> a = np.array([[1, 0],[0, 1]]) >>> b = np.array( [[4, 1],[2, 2]]) >>> np.dot(a,b) array([[4, 1],[2, 2]])
inner, outer	Calculate the inner and outer product of two arrays	>>> a = np.array([1, 1, 1]) >>> b = np.array([3, 5, 1]) >>> np.inner(a,b) 9
linalg.norm	Find a matrix or vector norm	>>> a = np.arange(3) >>> np.linalg.norm(a) 2.23606
linalg.det	Compute the determinant of an array	>>> a = np.array([[1,2],[3,4]]) >>> np.linalg.det(a) -2.0
linalg.inv	Compute the inverse of a matrix	>>> a = np.array([[1,2],[3,4]]) >>> np.linalg.inv(a) array([[-2., 1.],[1.5, -0.5]])
linalg.qr	Calculate the QR decomposition	>>> a = np.array([[1,2],[3,4]]) >>> np.linalg.qr(a) (array([[0.316, 0.948], [0.948, 0.316]]), array([[ 3.162, 4.427], [ 0., 0.632]]))
linalg.cond	Compute the condition number of a matrix	>>> a = np.array([[1,3],[2,4]]) >>> np.linalg.cond(a) 14.933034
trace	Compute the sum of the diagonal element	>>> np.trace(np.arange(6)). reshape(2,3)) 4

NumPy random numbers

An important part of any simulation is the ability to generate random numbers. For this purpose, NumPy provides various routines in the submodule random. It uses a particular algorithm, called the Mersenne Twister, to generate pseudorandom numbers.

First, we need to define a seed that makes the random numbers predictable. When the value is reset, the same numbers will appear every time. If we do not assign the seed, NumPy automatically selects a random seed value based on the system's random number generator device or on the clock:

>>> np.random.seed(20)

An array of random numbers in the [0.0, 1.0] interval can be generated as follows:

>>> np.random.rand(5)
array([0.5881308, 0.89771373, 0.89153073, 0.81583748, 
         0.03588959])
>>> np.random.rand(5)
array([0.69175758, 0.37868094, 0.51851095, 0.65795147,  
       0.19385022])

>>> np.random.seed(20)    # reset seed number
>>> np.random.rand(5)
array([0.5881308, 0.89771373, 0.89153073, 0.81583748,  
       0.03588959])

If we want to generate random integers in the half-open interval [min, max], we can user the randint(min, max, length) function:

>>> np.random.randint(10, 20, 5)
array([17, 12, 10, 16, 18])

NumPy also provides for many other distributions, including the Beta, bionomial, chi-square, Dirichlet, exponential, F, Gamma, geometric, or Gumbel.

The following table will list some distribution functions and give examples for generating random numbers:

Function	Description	Example
binomial	Draw samples from a binomial distribution (n: number of trials, p: probability)	>>> n, p = 100, 0.2 >>> np.random.binomial(n, p, 3) array([17, 14, 23])
dirichlet	Draw samples using a Dirichlet distribution	>>> np.random.dirichlet(alpha=(2,3), size=3) array([[0.519, 0.480], [0.639, 0.36], [0.838, 0.161]])
poisson	Draw samples from a Poisson distribution	>>> np.random.poisson(lam=2, size= 2) array([4,1])
normal	Draw samples using a normal Gaussian distribution	>>> np.random.normal (loc=2.5, scale=0.3, size=3) array([2.4436, 2.849, 2.741)
uniform	Draw samples using a uniform distribution	>>> np.random.uniform( low=0.5, high=2.5, size=3) array([1.38, 1.04, 2.19[)

We can also use the random number generation to shuffle items in a list. Sometimes this is useful when we want to sort a list in a random order:

>>> a = np.arange(10)
>>> np.random.shuffle(a)
>>> a
array([7, 6, 3, 1, 4, 2, 5, 0, 9, 8])

The following figure shows two distributions, binomial and poisson , side by side with various parameters (the visualization was created with matplotlib, which will be covered in Chapter 4, Data Visualization):

Summary

In this chapter, we covered a lot of information related to the NumPy package, especially commonly used functions that are very helpful to process and analyze data in ndarray. Firstly, we learned the properties and data type of ndarray in the NumPy package. Secondly, we focused on how to create and manipulate an ndarray in different ways, such as conversion from other structures, reading an array from disk, or just generating a new array with given values. Thirdly, we studied how to access and control the value of each element in ndarray by using indexing and slicing.

Then, we are getting familiar with some common functions and operations on ndarray.

And finally, we continue with some advance functions that are related to statistic, linear algebra and sampling data. Those functions play important role in data analysis.

However, while NumPy by itself does not provide very much high-level data analytical functionality, having an understanding of it will help you use tools such as Pandas much more effectively. This tool will be discussed in the next chapter.

Practice exercises

Exercise 1: Using an array creation function, let's try to create arrays variable in the following situations:

• Create ndarray from the existing data
• Initialize ndarray which elements are filled with ones, zeros, or a given interval
• Loading and saving data from a file to an ndarray

Exercise 2: What is the difference between np.dot(a, b) and (a*b)?

Exercise 3: Consider the vector [1, 2, 3, 4, 5] building a new vector with four consecutive zeros interleaved between each value.

Exercise 4: Taking the data example file chapter2-data.txt, which includes information on a system log, solves the following tasks:

• Try to build an ndarray from the data file
• Statistic frequency of each device type in the built matrix
• List unique OS that appears in the data log
• Sort user by provinceID and count the number of users in each province