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For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n + 1)/2 entries on and below the main diagonal. For such matrices, the half-vectorization is sometimes more useful than the ...
In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .
vector supports fast element insertion or removal at the end. Any insertion or removal of an element not at the end of the vector needs elements between the insertion position and the end of the vector to be copied. The iterators to the affected elements are thus invalidated. In fact, any insertion can potentially invalidate all iterators.
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 ...
A single-stranded non-circular DNA molecule has two non-identical ends, the 3' end and the 5' end (usually pronounced "three prime end" and "five prime end"). The numbers refer to the numbering of carbon atoms in the deoxyribose, which is a sugar forming an important part of the backbone of the DNA molecule.
If the 4th component of the vector is 0 instead of 1, then only the vector's direction is reflected and its magnitude remains unchanged, as if it were mirrored through a parallel plane that passes through the origin. This is a useful property as it allows the transformation of both positional vectors and normal vectors with the same matrix.
A double-ended queue can be used to store the browsing history: new websites are added to the end of the queue, while the oldest entries will be deleted when the history is too large. When a user asks to clear the browsing history for the past hour, the most recently added entries are removed.
Here, c[i:i+3] represents the four array elements from c[i] to c[i+3] and the vector processor can perform four operations for a single vector instruction. Since the four vector operations complete in roughly the same time as one scalar instruction, the vector approach can run up to four times faster than the original code.