DASUM

DASUM is a basic routine in the BLAS (Basic Linear Algebra Subprograms) library that computes the sum of the absolute values of the elements of a double-precision vector. It is a Level 1 BLAS operation and is implemented in many numerical libraries, including NetLIB BLAS, OpenBLAS, ATLAS, and Intel MKL. DASUM is commonly used to obtain the L1 norm of a vector or as a building block in more complex algorithms.

The function operates on a vector with a specified stride. In Fortran, the routine is typically declared as a function that returns a double precision value: DASUM(N, DX, INCX), where N is the number of elements to consider, DX is the array of double-precision elements, and INCX is the increment between elements of DX that are included in the sum. In the C interface, the equivalent is often exposed as cblas_dasum(N, X, INCX) or the legacy Fortran name dasum_, depending on the binding. The return value is the sum of the absolute values of the N elements X[i*INCX].

Formally, the operation is sum_{i=0}^{N-1} |X[i*INCX]|. If N <= 0, the result is 0.0. The increment INCX can be positive or negative, allowing traversal of the vector in forward or reverse order without copying data. The routine runs in O(N) time and uses a straightforward accumulation.

Related routines include SASUM (single precision) and SCASUM, as part of the same family of vector-norm computations. DASUM is widely used in numerical linear algebra for norm estimation, scaling checks, and normalization tasks.