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In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective , and if it exists, is denoted by f − 1 . {\displaystyle f^{-1}.}
The convex conjugate (specifically, the Legendre transform) of the softplus function is the negative binary entropy (with base e).This is because (following the definition of the Legendre transform: the derivatives are inverse functions) the derivative of softplus is the logistic function, whose inverse function is the logit, which is the derivative of negative binary entropy.
Since the function f(n) = A(n, n) considered above grows very rapidly, its inverse function, f −1, grows very slowly. This inverse Ackermann function f −1 is usually denoted by α. In fact, α(n) is less than 5 for any practical input size n, since A(4, 4) is on the order of .
The elementary functions are constructed by composing arithmetic operations, the exponential function (), the natural logarithm (), trigonometric functions (,), and their inverses. The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's ...
Hybrid Reverse Monte Carlo (HRMC) [19] [20] is a code capable of fitting both the pair correlation function and structure factor along with bond angle and coordination distributions. Unique to this code is the implementation of a number of empirical interatomic potentials for carbon (EDIP), silicon (EDIP [ 21 ] and Stillinger-Weber [ 22 ] ) and ...
A common type of implicit function is an inverse function. Not all functions have a unique inverse function. If g is a function of x that has a unique inverse, then the inverse function of g, called g −1, is the unique function giving a solution of the equation = for x in terms of y. This solution can then be written as
If a function is bijective (and so possesses an inverse function), then negative iterates correspond to function inverses and their compositions. For example, f −1 (x) is the normal inverse of f, while f −2 (x) is the inverse composed with itself, i.e. f −2 (x) = f −1 (f −1 (x)).
Inverse model of a reaching task. The arm's desired trajectory, Xref(t), is input into the model, which generates the necessary motor commands, ũ(t), to control the arm. Inverse models use the desired and actual position of the body as inputs to estimate the necessary motor commands which would transform the current position into the desired one.