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Stay on top of what's happening at IHS Markit. Below is the listing of the newest publications. AWS D Search complete list of new releases. Browse top new releases. Browse top sellers. Browse Publishers. It includes everything from short examples and tutorials to full-blown courses and books composed in the notebook format! Video tutorials Searching the Internet, you will find many video-recorded tutorials on IPython. As you go through the examples here and elsewhere, you can use it to familiarize yourself with all the tools that IPython has to offer.

For example, images—particularly digital images—can be thought of as simply two- dimensional arrays of numbers representing pixel brightness across the area. Sound clips can be thought of as one-dimensional arrays of intensity versus time. No matter what the data are, the first step in making them analyzable will be to transform them into arrays of numbers. For this reason, efficient storage and manipulation of numerical arrays is absolutely fundamental to the process of doing data science.

This chapter will cover NumPy in detail. NumPy arrays form the core of nearly the entire ecosystem of data science tools in Python, so time spent learning to use NumPy effectively will be valuable no matter what aspect of data science interests you. Once you do, you can import NumPy and double-check the version: In[1]: import numpy numpy. For example, to display all the contents of the numpy namespace, you can type this: In [3]: np. Understanding Data Types in Python Effective data-driven science and computation requires understanding how data is stored and manipulated.

This section outlines and contrasts how arrays of data are handled in the Python language itself, and how NumPy improves on this.

Users of Python are often drawn in by its ease of use, one piece of which is dynamic typing. Understanding how this works is an important piece of learning to analyze data efficiently and effectively with Python. But what this type flexibility also points to is the fact that Python variables are more than just their value; they also contain extra information about the type of the value.

This means that every Python object is simply a cleverly disguised C structure, which contains not only its value, but other information as well. Looking through the Python 3. Figure Notice the difference here: a C integer is essentially a label for a position in memory whose bytes encode an integer value.

This extra information in the Python integer structure is what allows Python to be coded so freely and dynamically. All this additional information in Python types comes at a cost, however, which becomes especially apparent in structures that combine many of these objects.

The standard mutable multielement container in Python is the list. In the special case that all variables are of the same type, much of this information is redundant: it can be much more efficient to store data in a fixed-type array.

The difference between a dynamic-type list and a fixed-type NumPy-style array is illustrated in Figure The Python list, on the other hand, contains a pointer to a block of pointers, each of which in turn points to a full Python object like the Python integer we saw earlier.

Again, the advantage of the list is flexibility: because each list element is a full structure containing both data and type information, the list can be filled with data of any desired type. The difference between C and Python lists Fixed-Type Arrays in Python Python offers several different options for storing data in efficient, fixed-type data buffers.

The built-in array module available since Python 3. Much more useful, however, is the ndarray object of the NumPy package. If types do not match, NumPy will upcast if possible here, integers are upcast to floating point : In[9]: np. Here are several examples: In[12]: Create a length integer array filled with zeros np.

Because NumPy is built in C, the types will be familiar to users of C, Fortran, and other related languages. The standard NumPy data types are listed in Table Note that when constructing an array, you can specify them using a string: np. While the types of operations shown here may seem a bit dry and pedantic, they comprise the building blocks of many other examples used throughout the book. Get to know them well! This means, for example, that if you attempt to insert a floating-point value to an integer array, the value will be silently truncated.

In this case, the defaults for start and stop are swapped. For example: In[24]: x2 Out[24]: array [[12, 5, 2, 4], [ 7, 6, 8, 8], [ 1, 6, 7, 7]] In[25]: x2[:2, :3] two rows, three columns Out[25]: array [[12, 5, 2], [ 7, 6, 8]] In[26]: x2[:3, ] all rows, every other column Out[26]: array [[12, 2], [ 7, 8], [ 1, 7]] Finally, subarray dimensions can even be reversed together: In[27]: x2[, ] Out[27]: array [[ 7, 7, 6, 1], [ 8, 8, 6, 7], [ 4, 2, 5, 12]] Accessing array rows and columns.

One commonly needed routine is accessing single rows or columns of an array. This is one area in which NumPy array slicing differs from Python list slicing: in lists, slices will be copies. Creating copies of arrays Despite the nice features of array views, it is sometimes useful to instead explicitly copy the data within an array or a subarray. The most flexible way of doing this is with the reshape method.

Where possible, the reshape method will use a no-copy view of the initial array, but with noncontiguous memory buffers this is not always the case. Another common reshaping pattern is the conversion of a one-dimensional array into a two-dimensional row or column matrix.

Array Concatenation and Splitting All of the preceding routines worked on single arrays. Concatenation of arrays Concatenation, or joining of two arrays in NumPy, is primarily accomplished through the routines np. Splitting of arrays The opposite of concatenation is splitting, which is implemented by the functions np. The related functions np. Computation on NumPy Arrays: Universal Functions Up until now, we have been discussing some of the basic nuts and bolts of NumPy; in the next few sections, we will dive into the reasons that NumPy is so important in the Python data science world.

Computation on NumPy arrays can be very fast, or it can be very slow. It then introduces many of the most common and useful arithmetic ufuncs available in the NumPy package. This is in part due to the dynamic, interpreted nature of the language: the fact that types are flexible, so that sequences of operations cannot be compiled down to efficient machine code as in languages like C and Fortran.

Each of these has its strengths and weaknesses, but it is safe to say that none of the three approaches has yet surpassed the reach and popularity of the standard CPython engine. A straightforward approach might look like this: In[1]: import numpy as np np.

But if we measure the execution time of this code for a large input, we see that this operation is very slow, perhaps surprisingly so! It turns out that the bottleneck here is not the operations themselves, but the type-checking and function dispatches that CPython must do at each cycle of the loop.

Introducing UFuncs For many types of operations, NumPy provides a convenient interface into just this kind of statically typed, compiled routine. This is known as a vectorized operation. You can accomplish this by simply performing an operation on the array, which will then be applied to each element.

This vectorized approach is designed to push the loop into the compiled layer that underlies NumPy, leading to much faster execution.

Ufuncs are extremely flexible—before we saw an operation between a scalar and an array, but we can also operate between two arrays: In[5]: np. Any time you see such a loop in a Python script, you should consider whether it can be replaced with a vectorized expression. Table The basic np.

A look through the NumPy documentation reveals a lot of interesting functionality. Another excellent source for more specialized and obscure ufuncs is the submodule scipy. If you want to compute some obscure mathematical function on your data, chances are it is implemented in scipy. Advanced Ufunc Features Many NumPy users make use of ufuncs without ever learning their full set of features. Specifying output For large calculations, it is sometimes useful to be able to specify the array where the result of the calculation will be stored.

Aggregates For binary ufuncs, there are some interesting aggregates that can be computed directly from the object. A reduce repeatedly applies a given operation to the elements of an array until only a single result remains.

Outer products Finally, any ufunc can compute the output of all pairs of two different inputs using the outer method. Another extremely useful feature of ufuncs is the ability to operate between arrays of different sizes and shapes, a set of operations known as broadcasting.

Summing the Values in an Array As a quick example, consider computing the sum of all values in an array. Multidimensional aggregates One common type of aggregation operation is an aggregate along a row or column.

Similarly, we can find the maximum value within each row: In[12]: M. The axis keyword specifies the dimension of the array that will be collapsed, rather than the dimension that will be returned. Some of these NaN-safe functions were not added until NumPy 1. Table provides a list of useful aggregation functions available in NumPy. We may also wish to compute quantiles: In[16]: print "25th percentile: ", np. Broadcasting is simply a set of rules for applying binary ufuncs addition, subtraction, multiplication, etc.

We can similarly extend this to arrays of higher dimension. While these examples are relatively easy to understand, more complicated cases can involve broadcasting of both arrays. The geometry of these examples is visualized in Figure Visualization of NumPy broadcasting The light boxes represent the broadcasted values: again, this extra memory is not actually allocated in the course of the operation, but it can be useful conceptually to imagine that it is.

Used with permission. The shapes of the arrays are: M. How does this affect the calculation? But this is not how the broadcasting rules work!

That sort of flexibility might be useful in some cases, but it would lead to potential areas of ambiguity. Centering an array In the previous section, we saw that ufuncs allow a NumPy user to remove the need to explicitly write slow Python loops. Broadcasting extends this ability.

Imagine you have an array of 10 observations, each of which consists of 3 values. Plotting a two-dimensional function One place that broadcasting is very useful is in displaying images based on two- dimensional functions. In NumPy, Boolean masking is often the most efficient way to accomplish these types of tasks. Example: Counting Rainy Days Imagine you have a series of data that represents the amount of precipitation each day for a year in a given city. What is the average precipitation on those rainy days?

How many days were there with more than half an inch of rain? Digging into the data One approach to this would be to answer these questions by hand: loop through the data, incrementing a counter each time we see values in some desired range. The result of these comparison operators is always an array with a Boolean data type. Working with Boolean Arrays Given a Boolean array, there are a host of useful operations you can do. Another way to get at this information is to use np.

For example: In[22]: are all values in each row less than 8? These have a different syntax than the NumPy versions, and in particular will fail or produce unintended results when used on multidimensional arrays. Be sure that you are using np.

But what if we want to know about all days with rain less than four inches and greater than one inch? For example, we can address this sort of compound question as follows: In[23]: np. Here are some examples of results we can compute when combining masking with aggregations: In[25]: print "Number days without rain: ", np. A more powerful pattern is to use Boolean arrays as masks, to select particular subsets of the data themselves. We are then free to operate on these values as we wish. When would you use one versus the other?

In Python, all nonzero integers will evaluate as True. For Boolean NumPy arrays, the latter is nearly always the desired operation. Fancy Indexing In the previous sections, we saw how to access and modify portions of arrays using simple indices e. For example: In[8]: row[:, np. Modifying Values with Fancy Indexing Just as fancy indexing can be used to access parts of an array, it can also be used to modify parts of an array.

For example: 82 Chapter 2: Introduction to NumPy www. The result, of course, is that x[0] contains the value 6. Why is this not the case? With this in mind, it is not the augmentation that happens multiple times, but the assignment, which leads to the rather nonintuitive results. So what if you want the other behavior where the operation is repeated?

For this, you can use the at method of ufuncs available since NumPy 1. Another method that is similar in spirit is the reduceat method of ufuncs, which you can read about in the NumPy documentation. Example: Binning Data You can use these ideas to efficiently bin data to create a histogram by hand.

For example, imagine we have 1, values and would like to quickly find where they fall within an array of bins. We could compute it using ufunc. A histogram computed by hand Of course, it would be silly to have to do this each time you want to plot a histogram. This is why Matplotlib provides the plt. To compute the binning, Matplotlib uses the np.

How can this be? If you dig into the np. Sorting Arrays Up to this point we have been concerned mainly with tools to access and operate on array data with NumPy.

This section covers algorithms related to sorting values in NumPy arrays. All are means of accomplishing a similar task: sorting the values in a list or array. Fortunately, Python contains built-in sorting algorithms that are much more efficient than either of the simplistic algorithms just shown.

Fast Sorting in NumPy: np. By default np. To return a sorted version of the array without modifying the input, you can use np. NumPy provides this in the np.

Within the two partitions, the elements have arbitrary order. Similarly to sorting, we can partition along an arbitrary axis of a multidimensional array: In[13]: np.

Finally, just as there is a np. With the pairwise square-distances converted, we can now use np. We can do this with the np. Visualization of the neighbors of each point Each point in the plot has lines drawn to its two nearest neighbors. At first glance, it might seem strange that some of the points have more than two lines coming out of them: this is due to the fact that if point A is one of the two nearest neighbors of point B, this does not necessarily imply that point B is one of the two nearest neighbors of point A.

Although the broadcasting and row-wise sorting of this approach might seem less straightforward than writing a loop, it turns out to be a very efficient way of operating on this data in Python.

You might be tempted to do the same type of operation by manually looping through the data and sorting each set of neighbors individually, but this would almost certainly lead to a slower algorithm than the vectorized version we used. Big-O Notation Big-O notation is a means of describing how the number of operations required for an algorithm scales as the input grows in size. Far more common in the data science world is a less rigid use of big-O notation: as a general if imprecise description of the scaling of an algorithm.

Big-O notation, in this loose sense, tells you how much time your algorithm will take as you increase the amount of data. For our purposes, the N will usually indicate some aspect of the size of the dataset the number of points, the number of dimensions, etc. Notice that the big-O notation by itself tells you nothing about the actual wall-clock time of a computation, but only about its scaling as you change N.

But for small datasets in particular, the algorithm with better scaling might not be faster. Creating Structured Arrays Structured array data types can be specified in a number of ways. Earlier, we saw the dictionary method: In[10]: np. The next character specifies the type of data: characters, bytes, ints, floating points, and so on see Table The last character or characters represents the size of the object in bytes.

For example, you can create a type where each element contains an array or matrix of values. Why would you use this rather than a simple multidimensional array, or perhaps a Python dictionary?

On to Pandas This section on structured and record arrays is purposely at the end of this chapter, because it leads so well into the next package we will cover: Pandas. Pandas is a newer package built on top of NumPy, and provides an efficient implementation of a DataFrame. As well as offering a convenient storage interface for labeled data, Pandas implements a number of powerful data operations familiar to users of both database frameworks and spreadsheet programs.

In this chapter, we will focus on the mechanics of using Series, DataFrame, and related structures effectively. We will use examples drawn from real datasets where appropriate, but these examples are not necessarily the focus. Details on this installation can be found in the Pandas documentation.

If you followed the advice outlined in the preface and used the Anaconda stack, you already have Pandas installed. Once Pandas is installed, you can import it and check the version: In[1]: import pandas pandas. For example, to display all the contents of the pandas namespace, you can type this: In [3]: pd.

Introducing Pandas Objects At the very basic level, Pandas objects can be thought of as enhanced versions of NumPy structured arrays in which the rows and columns are identified with labels rather than simple integer indices. As we will see during the course of this chapter, Pandas provides a host of useful tools, methods, and functionality on top of the basic data structures, but nearly everything that follows will require an understanding of what these structures are.

Series [0. The values are simply a familiar NumPy array: In[3]: data. For example, the index need not be an integer, but can consist of values of any desired type.

A dictionary is a structure that maps arbitrary keys to a set of arbitrary values, and a Series is a structure that maps typed keys to a set of typed values. This typing is important: just as the type-specific compiled code behind a NumPy array makes it more efficient than a Python list for certain operations, the type information of a Pandas Series makes it much more efficient than Python dictionaries for certain operations. For example, data can be a list or NumPy array, in which case index defaults to an integer sequence: In[14]: pd.

DataFrame as a generalized NumPy array If a Series is an analog of a one-dimensional array with flexible indices, a DataFrame is an analog of a two-dimensional array with both flexible row indices and flexible column names. Just as you might think of a two-dimensional array as an ordered sequence of aligned one-dimensional columns, you can think of a DataFrame as a sequence of aligned Series objects.

DataFrame as specialized dictionary Similarly, we can also think of a DataFrame as a specialization of a dictionary. Where a dictionary maps a key to a value, a DataFrame maps a column name to a Series of column data. For a DataFrame, data['col0'] will return the first column.

From a single Series object. Any list of dictionaries can be made into a DataFrame. DataFrame data Out[24]: a b 0 0 0 1 1 2 2 2 4 Even if some keys in the dictionary are missing, Pandas will fill them in with NaN i. As we saw before, a DataFrame can be constructed from a dictionary of Series objects as well: In[26]: pd. Given a two-dimensional array of data, we can create a DataFrame with any specified column and index names. If omitted, an integer index will be used for each: In[27]: pd.

DataFrame np. This Index object is an interesting structure in itself, and it can be thought of either as an immutable array or as an ordered set technically a multiset, as Index objects may contain repeated values. Those views have some interesting consequences in the operations available on Index objects. Index as ordered set Pandas objects are designed to facilitate operations such as joins across datasets, which depend on many aspects of set arithmetic.

These included indexing e. Data Selection in Series As we saw in the previous section, a Series object acts in many ways like a one- dimensional NumPy array, and in many ways like a standard Python dictionary. Examples of these are as follows: In[7]: slicing by explicit index data['a':'c'] Out[7]: a 0. Notice that when you are slicing with an explicit index i. Indexers: loc, iloc, and ix These slicing and indexing conventions can be a source of confusion.

For example, if your Series has an explicit integer index, an indexing operation such as data[1] will use the explicit indices, while a slicing operation like data[] will use the implicit Python-style index. First, the loc attribute allows indexing and slicing that always references the explicit index: In[14]: data.

The purpose of the ix indexer will become more apparent in the context of DataFrame objects, which we will discuss in a moment. Data Selection in DataFrame Recall that a DataFrame acts in many ways like a two-dimensional or structured array, and in other ways like a dictionary of Series structures sharing the same index.

These analogies can be helpful to keep in mind as we explore data selection within this structure. DataFrame as a dictionary The first analogy we will consider is the DataFrame as a dictionary of related Series objects. For example, if the column names are not strings, or if the column names conflict with methods of the DataFrame, this attribute-style access is not possible. DataFrame as two-dimensional array As mentioned previously, we can also view the DataFrame as an enhanced two- dimensional array.

We can examine the raw underlying data array using the values attribute: In[24]: data. For example, we can transpose the full DataFrame to swap rows and columns: In[25]: data. In particular, passing a single index to an array accesses a row: In[26]: data.

Here Pandas again uses the loc, iloc, and ix indexers mentioned earlier. Using the iloc indexer, we can index the underlying array as if it is a simple NumPy array using the implicit Python-style index , but the DataFrame index and column labels are maintained in the result: In[28]: data. For example, in the loc indexer we can combine masking and fancy indexing as in the following: In[31]: data. Pandas includes a couple useful twists, however: for unary operations like negation and trigonometric functions, these ufuncs will preserve index and column labels in the output, and for binary operations such as addition and multiplication, Pandas will automatically align indices when passing the objects to the ufunc.

We will additionally see that there are well-defined operations between one-dimensional Series structures and two-dimensional DataFrame structures. Series rng. DataFrame rng. UFuncs: Index Alignment For binary operations on two Series or DataFrame objects, Pandas will align indices in the process of performing the operation.

For example, calling A. Operations between a DataFrame and a Series are similar to operations between a two-dimensional and one-dimensional NumPy array. Handling Missing Data The difference between data found in many tutorials and data in the real world is that real-world data is rarely clean and homogeneous.

In particular, many interesting datasets will have some amount of data missing. Trade-Offs in Missing Data Conventions A number of schemes have been developed to indicate the presence of missing data in a table or DataFrame. Generally, they revolve around one of two strategies: using a mask that globally indicates missing values, or choosing a sentinel value that indicates a missing entry.

In the masking approach, the mask might be an entirely separate Boolean array, or it may involve appropriation of one bit in the data representation to locally indicate the null status of a value. In the sentinel approach, the sentinel value could be some data-specific convention, such as indicating a missing integer value with — or some rare bit pattern, or it could be a more global convention, such as indicating a missing floating-point value with NaN Not a Number , a special value which is part of the IEEE floating-point specification.

None of these approaches is without trade-offs: use of a separate mask array requires allocation of an additional Boolean array, which adds overhead in both storage and computation. Common special values like NaN are not available for all data types. As in most cases where no universally optimal choice exists, different languages and systems use different conventions. Missing Data in Pandas The way in which Pandas handles missing values is constrained by its reliance on the NumPy package, which does not have a built-in notion of NA values for non- floating-point data types.

While R contains four basic data types, NumPy supports far more than this: for example, while R has a single integer type, NumPy supports fourteen basic integer types once you account for available precisions, signedness, and endianness of the encoding. Further, for the smaller data types such as 8-bit integers , sacrificing a bit to use as a mask will significantly reduce the range of values it can represent.

With these constraints in mind, Pandas chose to use sentinels for missing data, and further chose to use two already-existing Python null values: the special floating- point NaN value, and the Python None object. This choice has some side effects, as we will see, but in practice ends up being a good compromise in most cases of interest.

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