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Moreover, complementary Python packages are available; SciPy is a library that adds more MATLAB-like functionality and Matplotlib is a plotting package that provides MATLAB-like plotting functionality. Although matlab can perform sparse matrix operations, numpy alone cannot perform such operations and requires the use of the scipy.sparse library.
CuPy is an open source library for GPU-accelerated computing with Python programming language, providing support for multi-dimensional arrays, sparse matrices, and a variety of numerical algorithms implemented on top of them. [3] CuPy shares the same API set as NumPy and SciPy, allowing it to be a drop-in replacement to run NumPy/SciPy code on GPU.
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. [33] Python is dynamically type-checked and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional ...
In some programming languages (including Ada, Perl, Ruby, Apache Groovy, Kotlin, Haskell, and Pascal), a shortened two-dot ellipsis is used to represent a range of values given two endpoints; for example, to iterate through a list of integers between 1 and 100 inclusive in Perl:
By "small" we mean that the function being integrated is relatively smooth over the interval [,]. For such a function, a smooth quadratic interpolant like the one used in Simpson's rule will give good results. However, it is often the case that the function we are trying to integrate is not smooth over the interval.
Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of. Numerical linear algebra uses properties of vectors and matrices ...
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
A simple example is fitting a line in two dimensions to a set of observations. Assuming that this set contains both inliers, i.e., points which approximately can be fitted to a line, and outliers, points which cannot be fitted to this line, a simple least squares method for line fitting will generally produce a line with a bad fit to the data including inliers and outliers.