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The Gaussian function is the archetypal example of a bell shaped function. A bell-shaped function or simply 'bell curve' is a mathematical function having a characteristic "bell"-shaped curve. These functions are typically continuous or smooth, asymptotically approach zero for large negative/positive x, and have a single, unimodal maximum at ...
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function , which is defined by the formula: [ 1 ]
Matplotlib (portmanteau of MATLAB, plot, and library [3]) is a plotting library for the Python programming language and its numerical mathematics extension NumPy.It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wxPython, Qt, or GTK.
The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
The function is named in honor of von Hann, who used the three-term weighted average smoothing technique on meteorological data. [6] [2] However, the term Hanning function is also conventionally used, [7] derived from the paper in which the term hanning a signal was used to mean applying the Hann window to it.
It can be expressed by numerous definitions, for example "0 for negative inputs, output equals input for non-negative inputs". The term "ramp" can also be used for other functions obtained by scaling and shifting , and the function in this article is the unit ramp function (slope 1, starting at 0).
Following is a step by step description of the algorithm execution for a small example graph. The source vertex is the vertex A and the radius of every vertex is equal to 1. At the beginning of the algorithm, all vertices except for the source vertex A have infinite tentative distances, denoted by δ {\displaystyle \delta } in the pseudocode.