ASUM

Asum is a routine name used in numerical linear algebra, most prominently in the Basic Linear Algebra Subprograms (BLAS) library, where it denotes the sum of the absolute values of the elements of a vector. The BLAS standard provides several typed variants: SASUM for single precision, DASUM for double precision, and CASUM/ZASUM for complex vectors.

Definition and parameters: Given a vector x with length n and stride incx, asum returns sum_{i=1}^n |x_i|, where x_i is the element reached by starting at the first element and stepping incx each time. If n is non-positive, the result is zero. The exact function signatures depend on the interface (for example, the CBLAS wrappers map SASUM, DASUM, CASUM, and ZASUM to the corresponding data types).

Usage and significance: The sum of absolute values computes the 1-norm of a vector and is used in a variety of numerical algorithms for convergence testing, norm estimation, and preconditioning, among other tasks. Its linear-time complexity makes it a simple and robust measure of vector magnitude, suitable for large-scale computations.

Notes: While asum is common in BLAS documentation, naming and availability can vary by library and language. In non-BLAS contexts, asum may appear as a legacy name for similar sum-of-absolute-values operations or as a symbolic reference to a generic summation.