incx

incx is a parameter used in the Basic Linear Algebra Subprograms (BLAS) library to describe the storage stride between successive elements of a vector x. It controls how the elements of x are accessed during vector operations, enabling work on sub-vectors, strided data, or reversed sequences without copying data. The value of incx is an integer and is typically supplied along with a vector length and other parameters to BLAS routines.

In BLAS Level 1 routines such as dot product, axpy, and copy, incx specifies how far to advance from one element of x to the next. For example, with incx = 1, the routine reads consecutive elements x[0], x[1], x[2], ...; with incx = 2, it reads x[0], x[2], x[4], ...; with incx = -1, it traverses x in reverse from the starting point.

The corresponding parameter for the other vector in many routines is incy. Together with the length n, these strides allow efficient operations on subarrays, slices, or non-contiguous data layouts, and support operations on memory-aligned or offset pointers common in high-performance computing. The starting element is the first element provided, and negative increments simply determine traversal direction; the routines do not copy data to realign memory.

Implementation and usage notes: incx must be a nonzero integer; a zero value would cause undefined behavior by repeatedly accessing the same element. Programmers frequently use incx to operate on every k-th element or to process a portion of a larger array without creating a new vector.

While incx appears most often in BLAS contexts, it is generally a library-specific term rather than a universal mathematical concept. It is a practical convention for describing data layout and access patterns in vector computations. See also BLAS, vector, strided memory access.