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Adept implements automatic differentiation using an operator overloading approach, in which scalars to be differentiated are written as adouble, indicating an "active" version of the normal double, and vectors to be differentiated are written as aVector.
Reverse accumulation traverses the chain rule from outside to inside, or in the case of the computational graph in Figure 3, from top to bottom. The example function is scalar-valued, and thus there is only one seed for the derivative computation, and only one sweep of the computational graph is needed to calculate the (two-component) gradient.
A typical vector implementation consists, internally, of a pointer to a dynamically allocated array, [1] and possibly data members holding the capacity and size of the vector. The size of the vector refers to the actual number of elements, while the capacity refers to the size of the internal array.
Lighting and reflection calculations, as in the video game OpenArena, use the fast inverse square root code to compute angles of incidence and reflection.. Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates , the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in ...
A graph and its transpose. In the mathematical and algorithmic study of graph theory, the converse, [1] transpose [2] or reverse [3] of a directed graph G is another directed graph on the same set of vertices with all of the edges reversed compared to the orientation of the corresponding edges in G.
It is, however, preferable to use an algorithm from the C++ Standard Library for such tasks. [1] [2] [3] The member function erase can be used to delete an element from a collection, but for containers which are based on an array, such as vector, all elements after the deleted element have to be moved forward to avoid "gaps" in the collection ...
Three similar vectors are in use that condense the inversions of a permutation into a vector that uniquely determines it. They are often called inversion vector or Lehmer code. (A list of sources is found here.) This article uses the term inversion vector like Wolfram. [13]
Delayed evaluation solves this problem, and can be implemented in C++ by letting operator+ return an object of an auxiliary type, say VecSum, that represents the unevaluated sum of two Vecs, or a vector with a VecSum, etc. Larger expressions then effectively build expression trees that are evaluated only when assigned to an actual Vec variable ...