Category: numpy

NumPy – Statistical Functions ”; Previous Next NumPy has quite a few useful statistical functions for finding minimum, maximum, percentile standard deviation and variance, etc. from the given elements in the array. The functions are explained as follows − numpy.amin() and numpy.amax() These functions return the minimum and the maximum from the elements in the given array along the specified axis. Example Live Demo import numpy as np a = np.array([[3,7,5],[8,4,3],[2,4,9]]) print ”Our array is:” print a print ”n” print ”Applying amin() function:” print np.amin(a,1) print ”n” print ”Applying amin() function again:” print np.amin(a,0) print ”n” print ”Applying amax() function:” print np.amax(a) print ”n” print ”Applying amax() function again:” print np.amax(a, axis = 0) It will produce the following output − Our array is: [[3 7 5] [8 4 3] [2 4 9]] Applying amin() function: [3 3 2] Applying amin() function again: [2 4 3] Applying amax() function: 9 Applying amax() function again: [8 7 9] numpy.ptp() The numpy.ptp() function returns the range (maximum-minimum) of values along an axis. Live Demo import numpy as np a = np.array([[3,7,5],[8,4,3],[2,4,9]]) print ”Our array is:” print a print ”n” print ”Applying ptp() function:” print np.ptp(a) print ”n” print ”Applying ptp() function along axis 1:” print np.ptp(a, axis = 1) print ”n” print ”Applying ptp() function along axis 0:” print np.ptp(a, axis = 0) It will produce the following output − Our array is: [[3 7 5] [8 4 3] [2 4 9]] Applying ptp() function: 7 Applying ptp() function along axis 1: [4 5 7] Applying ptp() function along axis 0: [6 3 6] numpy.percentile() Percentile (or a centile) is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall. The function numpy.percentile() takes the following arguments. numpy.percentile(a, q, axis) Where, Sr.No. Argument & Description 1 a Input array 2 q The percentile to compute must be between 0-100 3 axis The axis along which the percentile is to be calculated Example Live Demo import numpy as np a = np.array([[30,40,70],[80,20,10],[50,90,60]]) print ”Our array is:” print a print ”n” print ”Applying percentile() function:” print np.percentile(a,50) print ”n” print ”Applying percentile() function along axis 1:” print np.percentile(a,50, axis = 1) print ”n” print ”Applying percentile() function along axis 0:” print np.percentile(a,50, axis = 0) It will produce the following output − Our array is: [[30 40 70] [80 20 10] [50 90 60]] Applying percentile() function: 50.0 Applying percentile() function along axis 1: [ 40. 20. 60.] Applying percentile() function along axis 0: [ 50. 40. 60.] numpy.median() Median is defined as the value separating the higher half of a data sample from the lower half. The numpy.median() function is used as shown in the following program. Example Live Demo import numpy as np a = np.array([[30,65,70],[80,95,10],[50,90,60]]) print ”Our array is:” print a print ”n” print ”Applying median() function:” print np.median(a) print ”n” print ”Applying median() function along axis 0:” print np.median(a, axis = 0) print ”n” print ”Applying median() function along axis 1:” print np.median(a, axis = 1) It will produce the following output − Our array is: [[30 65 70] [80 95 10] [50 90 60]] Applying median() function: 65.0 Applying median() function along axis 0: [ 50. 90. 60.] Applying median() function along axis 1: [ 65. 80. 60.] numpy.mean() Arithmetic mean is the sum of elements along an axis divided by the number of elements. The numpy.mean() function returns the arithmetic mean of elements in the array. If the axis is mentioned, it is calculated along it. Example Live Demo import numpy as np a = np.array([[1,2,3],[3,4,5],[4,5,6]]) print ”Our array is:” print a print ”n” print ”Applying mean() function:” print np.mean(a) print ”n” print ”Applying mean() function along axis 0:” print np.mean(a, axis = 0) print ”n” print ”Applying mean() function along axis 1:” print np.mean(a, axis = 1) It will produce the following output − Our array is: [[1 2 3] [3 4 5] [4 5 6]] Applying mean() function: 3.66666666667 Applying mean() function along axis 0: [ 2.66666667 3.66666667 4.66666667] Applying mean() function along axis 1: [ 2. 4. 5.] numpy.average() Weighted average is an average resulting from the multiplication of each component by a factor reflecting its importance. The numpy.average() function computes the weighted average of elements in an array according to their respective weight given in another array. The function can have an axis parameter. If the axis is not specified, the array is flattened. Considering an array [1,2,3,4] and corresponding weights [4,3,2,1], the weighted average is calculated by adding the product of the corresponding elements and dividing the sum by the sum of weights. Weighted average = (1*4+2*3+3*2+4*1)/(4+3+2+1) Example Live Demo import numpy as np a = np.array([1,2,3,4]) print ”Our array is:” print a print ”n” print ”Applying average() function:” print np.average(a) print ”n” # this is same as mean when weight is not specified wts = np.array([4,3,2,1]) print ”Applying average() function again:” print np.average(a,weights = wts) print ”n” # Returns the sum of weights, if the returned parameter is set to True. print ”Sum of weights” print np.average([1,2,3, 4],weights = [4,3,2,1], returned = True) It will produce the following output − Our array is: [1 2 3 4] Applying average() function: 2.5 Applying average() function again: 2.0 Sum of weights (2.0, 10.0) In a multi-dimensional array, the axis for computation can be specified. Example Live Demo import numpy as np a = np.arange(6).reshape(3,2) print ”Our array is:” print a print ”n” print ”Modified array:” wt = np.array([3,5]) print np.average(a, axis = 1, weights = wt) print ”n” print ”Modified array:” print np.average(a, axis = 1, weights = wt, returned = True) It will produce the following output − Our array is: [[0 1] [2 3] [4 5]] Modified array: [ 0.625 2.625 4.625] Modified array: (array([ 0.625, 2.625, 4.625]), array([ 8., 8., 8.])) Standard Deviation Standard deviation is the square root of the average of squared deviations from mean. The formula for standard deviation is as follows −

NumPy – String Functions ”; Previous Next The following functions are used to perform vectorized string operations for arrays of dtype numpy.string_ or numpy.unicode_. They are based on the standard string functions in Python”s built-in library. Sr.No. Function & Description 1 add() Returns element-wise string concatenation for two arrays of str or Unicode 2 multiply() Returns the string with multiple concatenation, element-wise 3 center() Returns a copy of the given string with elements centered in a string of specified length 4 capitalize() Returns a copy of the string with only the first character capitalized 5 title() Returns the element-wise title cased version of the string or unicode 6 lower() Returns an array with the elements converted to lowercase 7 upper() Returns an array with the elements converted to uppercase 8 split() Returns a list of the words in the string, using separatordelimiter 9 splitlines() Returns a list of the lines in the element, breaking at the line boundaries 10 strip() Returns a copy with the leading and trailing characters removed 11 join() Returns a string which is the concatenation of the strings in the sequence 12 replace() Returns a copy of the string with all occurrences of substring replaced by the new string 13 decode() Calls str.decode element-wise 14 encode() Calls str.encode element-wise These functions are defined in character array class (numpy.char). The older Numarray package contained chararray class. The above functions in numpy.char class are useful in performing vectorized string operations. Print Page Previous Next Advertisements ”;

NumPy – Histogram Using Matplotlib ”; Previous Next NumPy has a numpy.histogram() function that is a graphical representation of the frequency distribution of data. Rectangles of equal horizontal size corresponding to class interval called bin and variable height corresponding to frequency. numpy.histogram() The numpy.histogram() function takes the input array and bins as two parameters. The successive elements in bin array act as the boundary of each bin. import numpy as np a = np.array([22,87,5,43,56,73,55,54,11,20,51,5,79,31,27]) np.histogram(a,bins = [0,20,40,60,80,100]) hist,bins = np.histogram(a,bins = [0,20,40,60,80,100]) print hist print bins It will produce the following output − [3 4 5 2 1] [0 20 40 60 80 100] plt() Matplotlib can convert this numeric representation of histogram into a graph. The plt() function of pyplot submodule takes the array containing the data and bin array as parameters and converts into a histogram. from matplotlib import pyplot as plt import numpy as np a = np.array([22,87,5,43,56,73,55,54,11,20,51,5,79,31,27]) plt.hist(a, bins = [0,20,40,60,80,100]) plt.title(“histogram”) plt.show() It should produce the following output − Print Page Previous Next Advertisements ”;

NumPy – Array Creation Routines ”; Previous Next 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. Sr.No. Parameter & Description 1 Shape Shape of an empty array in int or tuple of int 2 Dtype Desired output data type. Optional 3 Order ”C” for C-style row-major array, ”F” for FORTRAN style column-major array Example The following code shows an example of an empty array. Live Demo 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. 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. Sr.No. Parameter & Description 1 Shape Shape of an empty array in int or sequence of int 2 Dtype Desired output data type. Optional 3 Order ”C” for C-style row-major array, ”F” for FORTRAN style column-major array Example 1 Live Demo # 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 2 Live Demo 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] Example 3 Live Demo # 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. Sr.No. Parameter & Description 1 Shape Shape of an empty array in int or tuple of int 2 Dtype Desired output data type. Optional 3 Order ”C” for C-style row-major array, ”F” for FORTRAN style column-major array Example 1 Live Demo # array of five ones. Default dtype is float import numpy as np x = np.ones(5) print x The output is as follows − [ 1. 1. 1. 1. 1.] Example 2 Live Demo import numpy as np x = np.ones([2,2], dtype = int) print x Now, the output would be as follows − [[1 1] [1 1]] Print Page Previous Next Advertisements ”;

NumPy – Advanced Indexing ”; Previous Next It is possible to make a selection from ndarray that is a non-tuple sequence, ndarray object of integer or Boolean data type, or a tuple with at least one item being a sequence object. Advanced indexing always returns a copy of the data. As against this, the slicing only presents a view. There are two types of advanced indexing − Integer and Boolean. Integer Indexing This mechanism helps in selecting any arbitrary item in an array based on its Ndimensional index. Each integer array represents the number of indexes into that dimension. When the index consists of as many integer arrays as the dimensions of the target ndarray, it becomes straightforward. In the following example, one element of specified column from each row of ndarray object is selected. Hence, the row index contains all row numbers, and the column index specifies the element to be selected. Example 1 Live Demo import numpy as np x = np.array([[1, 2], [3, 4], [5, 6]]) y = x[[0,1,2], [0,1,0]] print y Its output would be as follows − [1 4 5] The selection includes elements at (0,0), (1,1) and (2,0) from the first array. In the following example, elements placed at corners of a 4X3 array are selected. The row indices of selection are [0, 0] and [3,3] whereas the column indices are [0,2] and [0,2]. Example 2 Live Demo import numpy as np x = np.array([[ 0, 1, 2],[ 3, 4, 5],[ 6, 7, 8],[ 9, 10, 11]]) print ”Our array is:” print x print ”n” rows = np.array([[0,0],[3,3]]) cols = np.array([[0,2],[0,2]]) y = x[rows,cols] print ”The corner elements of this array are:” print y The output of this program is as follows − Our array is: [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11]] The corner elements of this array are: [[ 0 2] [ 9 11]] The resultant selection is an ndarray object containing corner elements. Advanced and basic indexing can be combined by using one slice (:) or ellipsis (…) with an index array. The following example uses slice for row and advanced index for column. The result is the same when slice is used for both. But advanced index results in copy and may have different memory layout. Example 3 Live Demo import numpy as np x = np.array([[ 0, 1, 2],[ 3, 4, 5],[ 6, 7, 8],[ 9, 10, 11]]) print ”Our array is:” print x print ”n” # slicing z = x[1:4,1:3] print ”After slicing, our array becomes:” print z print ”n” # using advanced index for column y = x[1:4,[1,2]] print ”Slicing using advanced index for column:” print y The output of this program would be as follows − Our array is: [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11]] After slicing, our array becomes: [[ 4 5] [ 7 8] [10 11]] Slicing using advanced index for column: [[ 4 5] [ 7 8] [10 11]] Boolean Array Indexing This type of advanced indexing is used when the resultant object is meant to be the result of Boolean operations, such as comparison operators. Example 1 In this example, items greater than 5 are returned as a result of Boolean indexing. Live Demo import numpy as np x = np.array([[ 0, 1, 2],[ 3, 4, 5],[ 6, 7, 8],[ 9, 10, 11]]) print ”Our array is:” print x print ”n” # Now we will print the items greater than 5 print ”The items greater than 5 are:” print x[x > 5] The output of this program would be − Our array is: [[ 0 1 2] [ 3 4 5] [ 6 7 8] [ 9 10 11]] The items greater than 5 are: [ 6 7 8 9 10 11] Example 2 In this example, NaN (Not a Number) elements are omitted by using ~ (complement operator). Live Demo import numpy as np a = np.array([np.nan, 1,2,np.nan,3,4,5]) print a[~np.isnan(a)] Its output would be − [ 1. 2. 3. 4. 5.] Example 3 The following example shows how to filter out the non-complex elements from an array. Live Demo import numpy as np a = np.array([1, 2+6j, 5, 3.5+5j]) print a[np.iscomplex(a)] Here, the output is as follows − [2.0+6.j 3.5+5.j] Print Page Previous Next Advertisements ”;

NumPy – Array From Existing Data ”; Previous Next 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. Sr.No. Parameter & Description 1 a Input data in any form such as list, list of tuples, tuples, tuple of tuples or tuple of lists 2 dtype By default, the data type of input data is applied to the resultant ndarray 3 order C (row major) or F (column major). C is default The following examples show how you can use the asarray function. Example 1 Live Demo # 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] Example 2 Live Demo # 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 Live Demo # 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 Live Demo # 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)] 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. Sr.No. Parameter & Description 1 buffer Any object that exposes buffer interface 2 dtype Data type of returned ndarray. Defaults to float 3 count The number of items to read, default -1 means all data 4 offset The starting position to read from. Default is 0 Example The following examples demonstrate the use of frombuffer function. Live Demo 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. Sr.No. Parameter & Description 1 iterable Any iterable object 2 dtype Data type of resultant array 3 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 1 Live Demo # 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 2 Live Demo # 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.] Print Page Previous Next Advertisements ”;

NumPy – Introduction ”; Previous Next 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. Print Page Previous Next Advertisements ”;

NumPy – Array Attributes ”; Previous Next 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 Live Demo 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 Live Demo # 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. Live Demo import numpy as np 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 1 Live Demo # 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 2 Live Demo # 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 − [[[ 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 1 Live Demo # 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 2 Live Demo # 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 numpy.flags The ndarray object has the following attributes. Its current values are returned by this function. Sr.No. Attribute & Description 1 C_CONTIGUOUS (C) The data is in a single, C-style contiguous segment 2 F_CONTIGUOUS (F) The data is in a single, Fortran-style contiguous segment 3 OWNDATA (O) The array owns the memory it uses or borrows it from another object 4 WRITEABLE (W) The data area can be written to. Setting this to False locks the data, making it read-only 5 ALIGNED (A) The data and all elements are aligned appropriately for the hardware 6 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 The following example shows the current values of flags. Live Demo 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 Print Page Previous Next Advertisements ”;

NumPy – Ndarray Object ”; Previous Next 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) The above constructor takes the following parameters − Sr.No. Parameter & Description 1 object Any object exposing the array interface method returns an array, or any (nested) sequence. 2 dtype Desired data type of array, optional 3 copy Optional. By default (true), the object is copied 4 order C (row major) or F (column major) or A (any) (default) 5 subok By default, returned array forced to be a base class array. If true, sub-classes passed through 6 ndmin Specifies minimum dimensions of resultant array Take a look at the following examples to understand better. Example 1 Live Demo import numpy as np a = np.array([1,2,3]) print a The output is as follows − [1, 2, 3] Example 2 Live Demo # more than one dimensions import numpy as np a = np.array([[1, 2], [3, 4]]) print a The output is as follows − [[1, 2] [3, 4]] Example 3 Live Demo # 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 Live Demo # 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). Print Page Previous Next Advertisements ”;