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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 ...
A two-vector or bivector [1] is a tensor of type () and it is the dual of a two-form, meaning that it is a linear functional which maps two-forms to the real numbers (or more generally, to scalars). The tensor product of a pair of vectors is a two-vector. Then, any two-form can be expressed as a linear combination of tensor products of pairs of ...
Examples include type casts, [2] being able to obtain the address of any variable, local or global, and different types of integers with special promotion properties. However, the incorporation of C's lenient attitude towards types and type conversions can result in a Pascal that loses some or all of its type security.
With this substitution, vectors p are always the same as vectors z, so there is no need to store vectors p. Thus, every iteration of these steepest descent methods is a bit cheaper compared to that for the conjugate gradient methods. However, the latter converge faster, unless a (highly) variable and/or non-SPD preconditioner is used, see above.
On many common platforms, this use of pointer punning can create problems if different pointers are aligned in machine-specific ways. Furthermore, pointers of different sizes can alias accesses to the same memory, causing problems that are unchecked by the compiler. Even when data size and pointer representation match, however, compilers can ...
Consistency should be used when choosing the names to use for the variables; ρ should not be mixed with θ and so on. A three-dimensional vector, the magnitude of whose projection onto the xy -plane is 5 units, whose angle from the positive x -axis is π /9 radians (20°), and whose height from the xy -plane is 3 units can be specified in any ...
In general, two dyadics can be added to get another dyadic, and multiplied by numbers to scale the dyadic. However, the product is not commutative; changing the order of the vectors results in a different dyadic. The formalism of dyadic algebra is an extension of vector algebra to include the dyadic product of vectors. The dyadic product is ...
The most vexing parse is a counterintuitive form of syntactic ambiguity resolution in the C++ programming language. In certain situations, the C++ grammar cannot distinguish between the creation of an object parameter and specification of a function's type. In those situations, the compiler is required to interpret the line as a function type ...