Vector Arithmetic Operations

Suppose you have two lists of measurements and want to add their values position by position, or scale every value in one list by the same factor. These are mathematical operations on sequences of numbers. Since vector is a familiar way to hold a list of values, it is natural to ask whether it is also the right tool for that arithmetic. The key is to distinguish a general-purpose container from a type designed with numerical computation in mind.

The standard library’s vector is a broad-purpose mechanism for holding values. Its flexibility makes it useful with many kinds of data and helps it fit the library’s containers, iterators, and algorithms. That role is different from being a mathematical vector type: vector does not provide mathematical vector operations.

It would be easy to imagine adding arithmetic operations to vector. But adding operations alone would not address the deeper design trade-off. The generality and flexibility that make vector useful as a broad container also rule out certain optimizations that are considered essential for serious numerical work. In other words, the limitation is not merely a missing convenience: vector’s general-purpose design constrains the optimizations available for numerical computation.

For numerical computation, the standard library offers valarray, a vector-like template in the <valarray> header. It is less general than vector and is more amenable to optimization for numerical work. This is a deliberate trade: valarray gives up some of vector’s generality in exchange for a design better suited to numerical computation.