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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]
The cross product operation is an example of a vector rank function because it operates on vectors, not scalars. Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing ...
In computer programming, array slicing is an operation that extracts a subset of elements from an array and packages them as another array, possibly in a different dimension from the original. Common examples of array slicing are extracting a substring from a string of characters, the " ell " in "h ell o", extracting a row or column from a two ...
In Python, functions are first-class objects that can be created and passed around dynamically. Python's limited support for anonymous functions is the lambda construct. An example is the anonymous function which squares its input, called with the argument of 5:
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
Thus a one-dimensional array is a list of data, a two-dimensional array is a rectangle of data, [12] a three-dimensional array a block of data, etc. This should not be confused with the dimension of the set of all matrices with a given domain, that is, the number of elements in the array.
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
Plot of normalized function (i.e. ()) with its spectral frequency components.. The unitary Fourier transforms of the rectangular function are [2] = = (), using ordinary frequency f, where is the normalized form [10] of the sinc function and = (/) / = (/), using angular frequency , where is the unnormalized form of the sinc function.