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The codes for the different kind of matrices are reported below; the actual data are stored in a different format depending on the specific kind; e.g., when the code DI is given, the subroutine expects a vector of length n containing the elements on the diagonal, while when the code GE is given, the subroutine expects an n×n array containing ...
MFEM is a free, lightweight, scalable C++ library for finite element methods. Intel MKL, Intel Math Kernel Library (in C and C++), a library of optimized math routines for science, engineering, and financial applications, written in C/C++ and Fortran. Core math functions include BLAS, LAPACK, ScaLAPACK, sparse solvers, fast Fourier transforms ...
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
F retains the array features added in Fortran 90, and removes control statements that were made obsolete by structured programming constructs added to both FORTRAN 77 and Fortran 90. F is described by its creators as "a compiled, structured, array programming language especially well suited to education and scientific computing". [ 71 ]
A single program deck, with individual subroutines marked. The markings show the effects of editing, as cards are replaced or reordered. Many early programming languages, including FORTRAN, COBOL and the various IBM assembler languages, used only the first 72 columns of a card – a tradition that traces back to the IBM 711 card reader used on the IBM 704/709/7090/7094 series (especially the ...
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
New Fortran statements, such as FORALL, and the ability to create PURE (side effect free) procedures; Compiler directives for recommended alignment and distribution of array data (influenced by the earlier Fortran D [1] [2] and Vienna Fortran research efforts) Compiler directive for specifying processor arrangements (e.g., rank, extent, etc.)
Array handling is included in Fortran for two main reasons: the notational convenience it provides, bringing the code closer to the underlying mathematical form; for the additional optimization opportunities it gives compilers (although there are plenty of opportunities for degrading optimization too!).