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NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
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Python [24] [25] with well-known scientific computing packages: NumPy, SymPy and SciPy. [26] [27] [28] R is a widely used system with a focus on data manipulation and statistics which implements the S language. [29] Many add-on packages are available (free software, GNU GPL license). SAS, [30] a system of software products for statistics.
In Python, == compares by value. Python's is operator may be used to compare object identities (comparison by reference), and comparisons may be chained—for example, a <= b <= c. Python uses and, or, and not as Boolean operators. Python has a type of expression named a list comprehension, and a more general expression named a generator ...
Pandas' syntax for mapping index values to relevant data is the same syntax Python uses to map dictionary keys to values. For example, if s is a Series, s['a'] will return the data point at index a. Unlike dictionary keys, index values are not guaranteed to be unique. If a Series uses the index value a for multiple data points, then s['a'] will ...
In Python, the ellipsis is a nullary expression that represents the Ellipsis singleton. It's used particularly in NumPy, where an ellipsis is used for slicing an arbitrary number of dimensions for a high-dimensional array: [10]
Prefix sums are trivial to compute in sequential models of computation, by using the formula y i = y i − 1 + x i to compute each output value in sequence order. However, despite their ease of computation, prefix sums are a useful primitive in certain algorithms such as counting sort, [1] [2] and they form the basis of the scan higher-order function in functional programming languages.