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The cross product operation is an example of a vector rank function because it operates on vectors, not scalars. Matrix multiplication is an example of a 2-rank function, because it operates on 2-dimensional objects (matrices). Collapse operators reduce the dimensionality of an input data array by one or more dimensions. For example, summing ...
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
The types of objects that can be iterated across (my_list in the example) are based on classes that inherit from the library class ITERABLE. The iteration form of the Eiffel loop can also be used as a boolean expression when the keyword loop is replaced by either all (effecting universal quantification) or some (effecting existential ...
Automatic vectorization, in parallel computing, is a special case of automatic parallelization, where a computer program is converted from a scalar implementation, which processes a single pair of operands at a time, to a vector implementation, which processes one operation on multiple pairs of operands at once.
In this example, code block 1 shows loop-dependent dependence between statement S2 iteration i and statement S1 iteration i-1. This is to say that statement S2 cannot proceed until statement S1 in the previous iteration finishes. Code block 2 show loop independent dependence between statements S1 and S2 in the same iteration.
is a non-degenerate bilinear form, that is, : is a map which is linear in both arguments, making it a bilinear form. By ϕ {\displaystyle \phi } being non-degenerate we mean that for each v ∈ V {\displaystyle v\in V} such that v ≠ 0 {\displaystyle v\neq 0} , there is a u ∈ V {\displaystyle u\in V} such that
Loop unrolling, also known as loop unwinding, is a loop transformation technique that attempts to optimize a program's execution speed at the expense of its binary size, which is an approach known as space–time tradeoff. The transformation can be undertaken manually by the programmer or by an optimizing compiler.
Specifically, the for loop will call a value's into_iter() method, which returns an iterator that in turn yields the elements to the loop. The for loop (or indeed, any method that consumes the iterator), proceeds until the next() method returns a None value (iterations yielding elements return a Some(T) value, where T is the element type).